It’s the best job in the world, and there are clear (sometimes funded) paths you can follow.
You would normally expect to take a music degree. But then a number of routes are possible.
First, conventional teacher-training, leading to a PGCE (Post Graduate Certificate in Education). Homerton in Cambridge is one of the leading providers:
There are other training routes, through some of which you are paid a salary to train. Rated no.1 in the country, and outstanding by OFSTED, the King Edward’s Consortium offers these and exceptional teacher training in Birmingham:
The DfE provides much more detail at: