The London Institution, in Finsbury Circus, was first established in the Old Jewry, in 1806, and in 1807 was incorporated by royal charter. This building, an elegant stone structure, was erected in 1816, and contains, in addition to a noble library, reading-rooms, &c., a lecture-room, that approached by a noble staircase, is capable of containing 750 persons; its objects are similar to those of the Royal Institution, and it is conducted, with little variation, upon the same plan.
Mogg's New Picture of London and Visitor's Guide to it Sights, 1844
LONDON INSTITUTION, FINSBURY CIRCUS, (north side). A proprietory Institution, established in 1806, in Sir William Clayton's house, in the Old Jewry. The first stone of the present building (William Brooks, architect) was laid May 4th, 1815, and the building opened April 21st, 1819. The library, consisting of upwards of 60,000 volumes, is particularly rich in topographical works, collected while the late William Upcott (d. 1845) was librarian. Professor Porson, the first librarian, died in the rooms of the Institution in the Old Jewry, in 1808. The library is open from 10 in the morning till 11 at night, with the exception of Saturdays and Sundays; on the former of which it is closed at 3 o'clock, on the latter it is always shut.
Peter Cunningham, Hand-Book of London, 1850
see also Circulating Libraries in Dickens' Dictionary - click here