You could also have a look at www.musicteachers.co.uk
Where do you live (you can also PM me if you don't want to write this down for everyone to read), maybe I can help ...
As for what to look for in a teacher: Qualifications are a good thing to look out for, although they don't necessarily make a good teacher. But they give you an idea of how much time and effort that person spent on improving vocal and teaching skills.
Experience of course, although newly qualified teachers are sometimes "burning" more than older, very routined ones. But you can get completely bored young ones and really excited older ones, so you really have to "try out" that person, otherwise you won't know
Most of all: They should have a good technique themselves and sound healthy and well balanced. Although I do not permanently sing to my students because I don't want copycats, it is essential. Many students are not impressed with the way their teachers sound, and then I sometimes ask myself: "Why would you want to study with a person whose voice does not sound good to you?"
And also: You have to feel at ease with your teacher. It is no use if you feel constantly intimidated or have the feeling that the teacher just has a set program that is the same for every student. Every voice is individual and should be treated as such.
As for musical theatre singing: I worked as a musical theatre performer for years and only can say: You have to learn this technique with someone who knows what they are doing. Some classical singing teachers tell you that belting will do harm when it actually doesn't if learned properly. I don't mind if people stay off teaching it because they have never done it, but then they should actually keep their mouths shut about something they they obviously know nothing about (sorry for the rant, but it's sadly true).
I studied both classical and contemporary singing and can only say that both have their place, and both can be done horribly wrong ...