You will need to take and pass the following: BSA Level one surf instructor course, Beach Lifeguard qualification (or equivilant, check with BSA) also you must be enhanced checked for CRB certificate if you are working with young people.
There are as with most service sectors the odd mickey mouse provider which you would do well to stay clear of as they will regress your skills rather than progress them.
I always tell people to go and have a course with Barry Hall down in Newquay he is the guru of training surf coaches and you will get great value for money learning from him.
For your beach lifeguard qualification you can do this by joining your local surf lifesaving club and getting involved with excellent clubs such as Mumbles, Aberavon, St Agnes etc
Or you can do an intensive course with salt water training, Lusty glaze or Dean Gough @ Outer reef.
The CRB check can be done through the BSA or Local Council.
One last thing, you have to be a member of the BSA for all of the above to ensure you are a qualified surfing coach!
Good luck and happy surf coaching