The house was formerly the site of the hairdressers Michael John and the club is named for the portrait artist Sir Oswald Birley, the paternal grandfather of owner Robin Birley.[2] The interior was designed by Tom Bell and Bruce Cavell, featuring "Murano chandeliers, country house-like fireplaces and a cupola soaring to [a] cigar terrace".[2] Oswald's was created out of a need for vintage wines at more affordable prices.[2] The head chef is Gianluca Cossu, previously of 5 Hertford Street.[2]
Writing in The Times, Damien Whitworth described the club as "a private dining club that has become one of the capital's most exclusive havens for senior members of the government, deep-pocketed donors, stars of show business looking to party privately, and members of the royal family".[3] In early 2022 Oswald's was described by Annabel Sampson in Tatler as the "...most exclusive of London's private members' clubs".[1] Oswald's has no social media accounts.[1]