Here is a postcard showing the Camden Athenaeum:
Islington: Social and cultural activities', A History of the County of Middlesex: Volume 8: Islington and Stoke Newington parishes (1985), pp. 45-51 wrote:The Athenaeum, Camden Road, was built in 1871 at the junction of Camden and Parkhurst roads, after appeals for a literary and scientific institution for the area. The building of brick and terracotta was designed by F. R. Meeson in an Italianate style. It contained meeting halls, libraries, and a hall for theatrical and musical performances, seating 600. It was later taken over by Beale's, the caterers, as the Athenaeum hall. In 1912 and 1915 it housed an orchestral society and music teachers, and was used for concerts, and after the Second World War rehearsals were held there by Donald Wolfit's Advance Players Association. In 1955 the building was demolished and the site used for a petrol station. (fn 5)
fn. 5 Pevsner, Lond. ii. 239; docs. found in fndn. stone of Athenaeum, and Note on its Hist., in Islington libr.; Howard, Lond. Theatres, 16.
The Athenaeum Chess Club started at the Camden Athenaeum two years later in 1873. Much of its early history can be gleaned from sources such as The Westminster Papers, the Illustrated London News, and even that new kid on the block, the British Chess Magazine. One delightful story is how the Athenaeum persuaded the septuagenarian, Horwitz, to represent it in matches against other clubs: he insisted on spotting pawn and two against the whippersnappers representing the opposition on top board!
The Athenaeum Chess Club's full style is the "Camden Athenaeum, Westminster and Central Chess Club". In 1908 it merged with the Westminster CC; I am not aware of when it merged with the Central. One question that has eluded me so far is which "Westminster CC" this was, there were several over the years. One problem with some stories about old chess clubs is that they "closed". Closer inspection sometimes reveals that they actually "moved".
The Athenaeum has changed venue many times in the intervening years, and has met in central, rather than north, London for a century or so, now. It claims to be the oldest extant chess club in the capital; I know of no plausible challengers.