Rapha also run rides out from both their London shops (Soho and Spitalfields) although obviously there’s a bit more town to get through. They often “park-jump” through Hyde Park, Richmond Park & Bushy Park to get out round Windsor (via Windsor Great Park) from the Soho shop.
Otherwise, as mentioned, just head up to Crystal Palace one Sunday morning and there will be hundreds of riders from Dulwich Paragon, Brixton Cycles, London Phoenix and maybe a scattering of others, just see if you can join in with one of them – just check how quick they’re going to be cos they’ll split into fast, medium & slow groups or sometimes set off together then split into long, medium, short routes.