Unfortunately I don’t know of anywhere it’s possible to kitesurf in London. However there are some locations that are easily accessible, even without a car. There are a few great spots in Shoeburyness, Southend which are easily accessible by train (just over an hour from Liverpool Street) and Shoeburyness train station is only a few minutes walk from the beach. There’s also a few kitesurf schools there that you can book lessons with or hire kit from, Southend Kitesurfing, Richys Kitesurf School and Essex Kitesurf School are all down there.
The London Kitesurf Liftshare facebook group is a good place to look out for places to go and see if you can grab a lift from anyone.
Kite Addicts is a great website with a useful map with good information on kiting spots, tides and weather.