I think the most important thing is that you already like him, feel he is empathetic towards you, think he is being supportive - all of these will mean you can form a therapeutic alliance with him.
The BACP website is fine for finding a therapist, a lot are registered with UKCP and BCABP too.
He won't tell you what your issues are (neither will anyone else) as YOU already know
and he will help you decide how you want to deal with them - again not by telling you how to but by helping you identify how YOU want to.
What most people don't realise about therapy is that no one tells you what to do but instead helps you identify them for yourself and then helps you remove the obstacles for growth.
For example (a famous example from a well known therapist before anyone accuses me of breaking confidentiality) - the therapist noted that the client was having difficulty in stopping stealing small items from shops, the client talked about it a lot (at no point did the therapist say they should stop or tell them what they were doing was wrong - but did ask what they thought were the consequences if they carried on). The therapist gave the client $50 and said that when the urge came upon the client to steal they should pay for it out of this money instead.
In this (extreme) example the therapist helped the client identify they wanted to do something, let them identify the issues and consequences and then when they were having difficulty offered them a possible solution.
There are many things going on in this encounter but perhaps some of what stopped the client stealing (and they returned the $50 after a month as they had no use for it) was that their therapist showed them an alternative, trusted them that they didn't need and could stop (even when they didn't 'know' it fully themselves) and invested in them when they thought they couldn't.
This therapist helped them remove this obstacle for growth - and lots of obstacles can be achieved by talking about it when the client identifies what there issues are and what they want to work on.
In a roundabout way I'm saying that it really matters that you find a therapist you like - and it doesn't matter so much what their approach is (I use different techniques depending on the client)