Like Ian, the only Singers club I can recall Was run by Ewan McColl and Peggy Seeger. Firstly in the Princess Louise pub in Holborn, and then another pub that I can't rember the name of, but still in that Holborn Bloomsbury area.
Whether it started in the 50's I cannot say...(Being a little bit too young for pubs at the time!)
No doubt the power of Mudcat will prevail, and more info will be forthcoming.
Kilburn is certainly more likely a district where Joe Heaney might have performed. Always been a hotbed for Irish music.
I'll keep looking at this, an intriguing question.
Cheers Ralphie