I doubt if this is that, but there was an Office of Universal Information, Agency, and Reference in 19 Catherine Street in London, in 1848. (The blurb at the back of the link above has a list of qualifications which seem inconsistent with "every conceivable question", however.) Its managing director was J.H. Stoqueler, who seems to have a lived a more interesting life than mine.
Closer in time to Sylvester is a derogatory 1887 reference to a UIS in the Saturday Review of Literature, Politics, Science and Art, March 26 1887, p.445, column 1.
Mr. Gladstone, who had come down on Tuesday afternoon,
made a theatrical entry bearing a large volume suggestive of the
mock-books of explosives carried by the St. Peterburg anachists,
and feigned to be very busy in taking notes, Mr. Childers
assisting him somewhat after the fashion of the unfortunate
bearers of the desks of the Universal Information Society who
perambulate the streets.
The picture this conjures up, of itinerant know-it-alls from Laputa carrying desks in the streets, makes me want more information.
According to a column "General Foreign Notes" in the Boston fortnightly review, The Literary World_, Sept6, 1884, p. 297:
An office for "universal information" has been opened near the British Museum. You pay your shilling, and ask your question, and get your answer.
The temporal proximity makes me think this might be the factual basis of Sylvester's 1885 reference, and the 1887 parliamentary report. A similar enterprise shows up in the Feb 1 1890 issue of The Athenaeum
UNIVERSAL INFORMATION BUREAU -- QUESTIONS ANSWERED on all SUBJECTS -- Fees from 1s -- FRANK HALLER, 56 Chancery Lane, W.C., Letters only.
And the Jan 29 1887 Illustrated London News has, in what I suppose is an "agony column" or Victorian analogue of a Stack Exchange post, (on p. 112) this comment:
“E. M. J." who wishes me to tell him the value of a genuine Mulready's cheap postage envelope, is referred to the Universal Information Office, Southampton-street, Bloomsbury. Down with the “dust,” “E. M. J.” (one shilling sterling), and the Southampton-street Bureau will tell you the cause of thunder; the meaning of the proverb, “‘Bate me an ace, quoth Bolton"; and why we should say, “Dancing the Hays," instead of “Dancing the Hay.” -