Fitters do come from the Motor industry, Aviation, Military. All sorts really.
Apprenticeships are the best way, but a very competitive entry. Check out GTR's page on engineering apprentices (not currently open, but it's an annual intake, historic adverts are still online).
If you're looking specifically for courses, anything in the mechanical or electrical engineering world will look good. Lots of vocational courses which provide hands on experience exist. Not a lot of fitters (in my experience) are degree educated, so Level 4/5 such as HNC, HND are a good level to look at.
Teesside University for example have good electrical engineering HNC/HND qualifications, I've heard.
Provided you have the base level GCSEs including Maths and English, there are many avenues to take, to get into railway engineering!