Building From 11/11/1942 To 9/1/1946
Club for the American forces in the UK during WW2. Also known as the American Red Cross Club. This is where those "oversexed, overpaid and over here" GIs hung out.
From British History online: The club occupied two buildings: 23 Shaftesbury Avenue, on the corner with Denman Street, previously Maison Lyons (a different branding for a Lyons Corner House), and the next door building, the extension to Cafe Monico. We believe both buildings were erected in 1888-9, no. 23, Piccadilly House, having "a fussy elevation" and both had been demolished by 1963. The whole block is now (2014) a pretty grim building of offices, fast food and tourist tat shops.
The club opened on Wednesday 11 November. This seems an odd choice, it having been the national memorial day since immediately after WW1, only 23 years previous.
The Guardian describes the activities the club provided. Hell's Angels contains the innocent reminiscences of an English dance hostess who volunteered there, while JCS-group paints a less chaste picture. British Pathe footage of the closing ceremony - a jovial and crowded 'GI Jamboree'.
The 1945 film “I live in Grosvenor Square”, about a American soldier's experience in England during the war, features Rainbow Corner. The exterior appears in the opening credits and there are a few scenes set inside. Though almost certainly shot in the studio, these do give an idea of what the place was like.