Improvisational piano teacher in London

I've been pootling around on the piano for a couple of years, but I need a teacher. The trouble is, I'm looking for quite a specific thing. I don't read music, I'm interested in being able to play different genres of improvised music and accompaniments, to interpret what other musicians are playing and generally play around in pleasing ways. I'm looking to learn patterns and shapes that I can reuse and combine, to make my improvisations harmonically richer and more rhythmic.

Specific styles I'd like to grasp are:
* gospel piano
* pop piano (think Carole King, Randy Newman, Elton John)
* jazz ballads (I don't want to show off, I want to play Gershwin and Billie Holiday songs slowly and beautifully)
* ragtime piano (I harbour a secret dream to accompany Buster Keaton movies on the piano)

I practice and I'm very enthusiastic if taught well, and I have a genuine passion for making music. And I'm convinced there's someone out there who can really help me learn all this - whether it's a good teacher or a more advanced learner.

Any takers?