I know a lot of harpers, although I don't play myself.

When finding a harp teacher, it is important that you find someone who teaches you good technique. You don't want to develop back trouble, shoulder trouble or wrist trouble from learning bad posture. And you don't want to discover down the road that you can't play fast or play fancy because you have developed bad habits.

You should be able to find a teacher who can teach you both to read music and to improvise. Many, many people do that.

There's no need for your teacher to be passionate about English folk music. What's important is that your teacher do her job well and do right by you as you learn to play.

Once good source of genuinely English music would be the Playford dances, (which Google.)

Best of luck with your new instrument.