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When I get enquiries from adult students I often suggest they come for an initial consultation free of charge to see how we get on. Some teachers will do this but you can't expect it as a matter of course. However, how you hit it off personally is important, I think.
It's very important. I offer 2 or 3 one-off lessons (ie at the usual rate but no commitment) as a start-up, when we discuss what the student would like to do, why they want to learn and what sort of music they would like to play. We assess their level and I make suggestions about what we might do. It's up to the student to decide whether to take lessons any further.
I'm on the edge of London so probably not near enough - but you could look on www.musicteachers.co.uk (which AnotherPianist mentioned) or
the EPTA uk site, which is:
www.epta-uk.org
good luck