Hmmm, hard to say. London is notorious for paying badly & not appreciating live music, sadly. The 100 Club in Oxford Street is the most obvious place I guess, lots of visiting US artists play there (Anson Funderburgh etc.). Possibly The Borderline down Charing Cross Road - mostly rock bands, but John Hammond has played there a few times.
But you can never tell. My mother lives in a little place called New Milton, on the south coast, near Bournemouth. They once had a Spanish blues band called The Lazy Jumpers playing at the local Arts Centre, so I went down to see them. Very good band, kinda similar to the stuff you play. Yet I don't think they ever played in London, so how they got this obscure little gig in the middle of nowhere, I have no idea.