There are several events, including Kingston and Richmond Rapidplays, coming up which might interest you.
3rd Kingston Rapidplay Chess Tournament @ Richard Mayo Centre Kingston United Reform Church Eden Street Kingston
Jun 1 @ 10:30 am – 6:00 pm
Golders Green FIDE Rapid Chess @ St Luke’s Church, Kidderpore Avenue, London
Jun 8 @ 10:30 am – 5:45 pm
Pimlico Summer Tournament @ Community Hall, Under Morgan House, 57 Vauxhall Bridge Road, London
Jun 13 @ 6:30 pm – 9:30 pm