Central st martins in London is the top BUT its won't wow you with facilities, it's very hard to get into. I would say it's for an edgy very worldly student.
Despite many courses being fashion design they are really different depending on the uni/ college. For example some will teach very technical pattern cutting with a leaning more towards tailoring and tradition and some the more creative out there is preferred.
I'm going to put this out there if the student is good they will probably get a 1st at a college outside London. London colleges take the best students and the work is generally a higher level. So is it better to be a big fish in a small pond or not? Really depends what you want to do with it after. I know people from my fashion course who are designers now some high street, some have their own labels. The ones with labels I'm not sure if they make money, it's low key and they are the ones with very rich parents. Did their MA's in New York , weren't particularly talented but you need the money behind you and determination which they do have.
You can also do well at from the following
London college of fashion
Ravensbourne college ( Greenwich)
Plus there are different pathways within fashion .. menswear,womenswear, printed textiles , knitwear, footwear.
I don't know about outside London. I have friends that went to UCA down in Kent and loved it, but haven't done much in fashion since.