Funnily enough I am currently on a years diploma studying cheesemaking!
The place I'm studying at is called The School of Artisan Food, I couldn't suggest a better place, there are a whole range of courses varying between one day through to a week, through to a year. They not only do Dairying but also Bakery, butchery, chocolate, brewing you name it. If it's artisan then they'll be doing it! It's in Nottingham though.
The West Highland Dairy is a lady called Cathy Biss and I have heard very good things about her (my head tutor has known her for many, many years). It is known to be very highly regarded in the Dairy industry. There is also another, Chris Ashby, AB Cheesemaking, well structured courses which are held at Reaseheath College, Nantwich, Cheshire.
However I have spent many years on my quest for fine cheese and depending on what your reason is for learning the craft most cheesemakers are happy to have you help them for a wee while or even pop in for a day and just observe. Of course if you are planning on opening a dairy next door to them then this might not be the case!
Here are the addresses that might be of help:
http://www.schoolofartisanfood.org/http://www.westhighlanddairy.co.uk/http://www.abcheesemaking.co.uk/index.aspMcR