Unless you're particularly generous with your definition of 'around London' I'd say no.
If you go to
Elcas - Enhanced Learning Credit Administration System you can search the database of learning providers. It's not particularly user friendly these days as you can't just browse the whole thing, however plugging 'helicopter' in as a search time gives 7 results.
Three are for ground schools, of the four that offer flying training two appear to be near Yorkshire, one is at Blackbushe and the other at Goodwood.
If you don't fancy those, you can suggest to a more conveniently located flying school that they might like to register as a Learning Provider. There's a link on the same website so they can start the registration process, not sure how long it takes though.