Hackney coaches abound in the metropolis, and are to be met with at all the regularly appointed stands. A knowledge of the fares or charges will best be gathered from a small work, a multum in parvo upon this subject, that, under the title of Mogg's Hackney Coach Fares, supplies information of great value to all who have occasion to use those vehicles; an assertion the truth of which is attested by the following critique, extracted from the columns of the Times: -"All who enter a hackney coach, or a hackney wherry, should use Mogg's Book of Fares: it is accurate and portable, and prevents the necessity of application to police-offices." This is to be obtained, with the best information upon the subject, of E. Mogg, No. 14, Great Russell Street, Covent Garden. Cabriolets of an extremely convenient form have lately been introduced; and the fares for these being two thirds of the hackney coach fares, the work just noticed supplies upon that subject all the requisite information. 

Mogg's New Picture of London and Visitor's Guide to it Sights, 1844

CABS. The fares are eightpence a mile. For any distance under a mile you must pay at the rate of a mile. For every half-mile (after the first mile) you pay fourpence, or half fare. A driver can refuse to take more than two persons in his cab.

Peter Cunningham, Hand-Book of London, 1850

Cabs. By an Act of Parliament (16 and 17 Victoria, c. 33), - which, for 1s., may be obtained from any respectable bookseller, the cabs and hackney carriages of London were subjected to stringent regulations, whose enforcement largely adds to the security and comfort of their patrons. There are, probably, in London about 4300 cabs, which daily convey from one part of the Metropolis to another some 50,000 passengers, at a yearly cost to the public of nearly 900,000l. These cabs are usually hired by their drivers, at a daily rate of 9s. to 12s., from the large cab-owners, and are divided into "two-wheelers" (Hansoms) and "four-wheelers;" the former accommodating two, and the latter four or five persons.
    Fares are calculated (1) by "distance," or (2) by "time."
    1. DISTANCE FARES  - 6d. per mile, or part of a mile, for two persons, within a four miles radius of Charing Cross.
    1s. per mile, or part of a mile, for every mile, or part of a mile, beyond four miles from Charing Cross.
    For every additional adult carried, beyond two persons, 6d. extra for the whole distance. Two children, under ten years of age, are counted as one adult.
    2. TIME FARES (for two persons).-For any time not exceeding one hour, 2s.; and for every fifteen minutes, or less than fifteen minutes, over the hour, 6d.
    1s. for every mile, or part of a mile, beyond four miles (radius) from Charing Cross.
    The driver is required to drive at a rate not exceeding four miles an hour. If ordered to drive with greater speed, be may claim 6d. a mile, or portion of a mile, in addition to his time-fare.
    For additional passengers, beyond two persons, the extra fare is 6d. each passenger for the whole hiring.
    Back-fare cannot be charged.
    6d. may be charged for every fifteen minutes during which the cab is detained by the hirer. This applies only to engagements by distance.
    The driver can be compelled to hire his carriage for a "time fare" between 8 p.m. and 6 a.m.
    LUGGAGE.-  A reasonable quantity is required to be carried free of charge, except when more than two persons are carried inside, and then 2d. may be demanded for every package placed outside.
    DISPUTES.- In case of any dispute between driver and hirer, the latter may require the driver to drive to the nearest Metropolitan Police Court, where the complaint will be immediately investigated. If no magistrate be sitting, the hirer may be driven to the nearest Police Station, where the case will be duly entered for the magistrate to decide at his next sitting.
    For luggage lost, apply at the chief Police Office, Scotland Yard, Parliament Street.
    The Hansom cabs are the most expeditious; but it is customary to reward their drivers with a trifle more than the legal fare.
    In London there are 218 cab-stands, 39 of which are within the City precincts.

Cruchley's London in 1865 : A Handbook for Strangers, 1865

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Cabs.—The cab laws of London are now except with regard to the distinctions drawn somewhat arbitrarily here and there between four-wheelers and hansoms, very simple and easy to be remembered. The main points to bear in mind are: that luggage carried outside is always to be paid for; that hansoms, though charged at the same rate as "growlers" when hired by distance—which is almost the on]y time when there is any particular gain in hiring them— cost 6d. an hour more when hired by time, and 8d. an hour more when standing still; and that you cannot make a man drive you about by the hour for more than one hour at a time. As for calculating fares, that must depend entirely on our own power of judging distance. Some people when in doubt take the driver's ticket and tell him to name his own fare; and when he is satisfied that he will be summoned if he be found to have overcharged, the plan is no doubt efficacious. The difficulty is to impress that conviction on his mind. A better plan is to judge by the time occupied and at will be found that about 1d. per minute is fair to both parties For 15 minutes 1s. 6d. should be paid, but 14 minutes may be taken to be within the 1s. This is not an official rate, but it will save trouble and generally prove right. It is as well to start with the clear understanding that, doubtful character as cabbie too often is, he is really by no means so black a sheep as be is sometimes painted. A hirer should always observe the number of a cab. If he leave any property in a cab be will possibly find it next day at the Lost Property Office, Great Scotland-yard, when, on payment of a percentage on the estimated value as a reward to the cabman for his honesty, he can obtain it back again. The following are the fares and general regulations as laid down by the Commissioners of Police:
FARES BY DISTANCE – 
If hired and discharged within the four-mile circle, for any distance not exceeding two miles – 1/-
… and for every additional mile of part of a mile – 6d
If hired, outside the four-mile circle, wherever discharged, for the first and each succeeding mile or part of a mile – 1/-
If hired within, but discharged outside, the four-mile circle, not exceeding one mile, 1s; exceeding one mile, then for each mile within the circle, 6d; and for each mile or part of a mile outside 1/-
FARES BY TIME – 
Inside the four-mile circle. Four-wheeled cabs, for one hour or less, 2s. Two-wheeled cabs, 2/6.
For every additional quarter of an hour or part of a quarter, four-wheeled cab, 6d; if a two-wheeled cab, -/8
If hired outside the circle, wherever discharged, for one hour or less, 2/6
If above one hour, then for every quarter of an hour or less -/8
If hired within, but discharged outside, the four-mile circle, the same.
EXTRA PAYMENTS – 
Hirers of Cabs should be particular in noticing these regulations, as disputes generally arise from their not being clearly understood.
Whether hired by distance or by time:
LUGGAGE. – For each package carried outside the carriage -/2
EXTRA PERSONS –
For each above two -/6
For each child under 10 years old -/3
By distance – WAITING :
For every 15 minutes completed:
If hired within the four-mile circle, four-wheels, 6d; two wheels -/8
If hired without circle, two or four wheels, -/8
GENERAL REGULATIONS.— 
Fares are according to distance or time, at the option of the hirer, expressed at the commencement of the hiring; if not otherwise expressed, the fare to be paid according to distance.
Driver, if hired by distance, is not compelled to drive more than six miles ; nor, if hired by time, to drive for more than one hour.
Agreement to pay more than legal fare is not binding; any sum paid beyond the fare may be recovered back.
Driver not to charge more than the sum agreed on for driving a distance, although such distance be exceeded by the driver.
If the driver agreed beforehand to take any sum less than the proper fare, the penalty for exacting or demanding more than the suns agreed upon is 40s.
The proprietor of every hackney carriage shall keep distinctly painted, both on the inside and outside, a table of fares ; and the driver shall have with him, and when required produce, the Authorised Book of Fares.
In case of any dispute between the hirer and driver, the hirer may require the driver to drive to the nearest metropolitan police-court or justice-room, when the complaint may be determined by the sitting magistrate without summons; or if no police-court or justice- room be open at the time, then to the nearest police station, where the complaint shall be entered, and tried by the magistrate at his next sitting
Every driver of any hackney carriage shall, when hired, deliver to the hirer a card printed according to the directions of the Commissioner of Police.
All property left in any hackney carriage shall be deposited by the driver at the nearest police station within twenty-four hours if not sooner claimed by the owner; such property to be returned to the person who shall prove to the satisfaction of the Commissioner of Police that the same belonged to him, on payment of all expenses incurred, and of such reasonable sum to the driver as the Commissioner shall award.
Cabmen's Shelters erected by the committee of the Cabmens Shelter Fund, with the hours each shelter is open

Archer-street,Westborne-grove, 12 noon to 2 am.
Clapham-common, 11 a.m. to 11 pm.
Eaton-square, 11 a.m to 11 p.m
Great Western Railway, Paddington, 10 a.m. to 10 p.m.
Hampstead, 10 a.m. to 10 p.m.
Harrow-road, 10 a.m, to 10 pm.
High Holborn, day and night.
Kensington, 11 a.m. to 11 p.m.
Kensington-park-road, 11 a.m. to 11 p.m.
Knightsbridge, day and night.
Ladbroke-grove-road, Notting Hill, 11 am, to 11 p.m.
Maida Vale, 10 am. to 10 p.m.
Palace-yard, 10 a.m. to 10 pm., and day and night during sessions of Parliament.
Park-road, Regent's-park, day and night.
Piccadilly (opposite Half-Moon-street), day and night.
Pickering-place, Bayswater, 10 am, to 10 p.m.
Pont-street, Belgrave.square, 10 am, to 10 p.m.
St. Clement Danes, day and night.
South Kensington, 11 a.m. to 11 p.m.
Vauxhall Station, 11 a.m. to 11 p.m.
Waterloo Station, 9 a.m. to 9 p.m.

Charles Dickens (Jr.), Dickens's Dictionary of London, 1879

CABS. The hiring of these vehicles may be either by distance or by time, at the option of the hirer, expressed at the commencement of the hiring, but unless so expressed to be by time, the fare is always to be reckoned by distance. -
    Fares by Distance. If hired and discharged within a radius of four miles from Charing Cross. For any distance not exceeding two miles, 1s.; for every additional mile or part of a mile, 6d. If hired outside four mile circle, wherever discharged, is. for each mile or part of a mile. If hired within and discharged outside four mile circle, for each mile ended within, 6d.; for each mile ended outside circle, 1s.; for any part of a mile ended outside over and above any number of miles completed, 1s. The driver cannot be compelled to drive more than six miles.
    Fares by Time. For one hour or less, Four wheel cabs, 2s. ; Two wheel cabs, 2s. 6d.; for every additional quarter of an hour or part, 6d. and 8d. respectively. If hired outside Four mile Circle, for either class of cab, 2s. 6d. for one hour or less; 8d. for every additional quarter of an hour or part. The driver cannot be compelled to drive for longer than one hour, or at a rate exceeding four miles an hour.
    Extra Persons. For every person above two, 6d. extra for the whole distance. Two children, under ten years of age, count as one person.
    Luggage carried outside cab, 2d. for each package.
    Waiting. For every fifteen minutes completed, 6d. for Four wheel cab; 8d. for Two wheel cab.
    In case of dispute, the hirer may require the driver to drive to the nearest Police Court, where the Magistrate, if sitting, will hear and decide. Articles left in cabs must be taken without delay to the Chief Police Office, Scotland Yard, Whitehall. where, in case of loss, application should at once be made.

for list of cab fares see: (1)  (2)  (3)  (4)  (5)  (6)

Reynolds' Shilling Coloured Map of London, 1895