The Reform Club
was originally a private gentlemen's club on the south side of Pall Mall (at number 104), in central London.
Wikipedia

Mr. Phileas Fogg
lived, in 1872, at No. 7, Saville Row, Burlington Gardens, the house in which Sheridan died in 1814.
He was one of the most noticeable members of the Reform Club,
though he seemed always to avoid attracting attention; an enigmatical personage,
about whom little was known, except that he was a polished man of the world.
Chapter I - In Which Phileas Fogg and Passepartout Accept Each Other