All the best races are either open (UK Cross Challenge) or club based (Nationals, Regionals, road relays, cross country relays). Collegiate (or University as we would have it) races are pretty mediocre on the whole. There are a number of cross country relay races (Uni Relays Series) which have some decent runners in (some very good runners in fact), but are pretty mixed ability. The BUSA (British Uni Champs) is the best standard Uni race, and that is not the best in the UK by any stretch (though, again, there will be a few good runners at the front).
There are a few universities which do bursaries, but these are nowhere near as lucrative as I believe the US colleges are, and you will usually need to get into the Uni on academic results and then apply for money once you start the course.
Only a few unis have actual coaches, though many will have an informal link with local clubs who will have coaches there.
Essentially, UK is split into regions for races. I think Scotland is split into 2 (East and West, but I don't know), then there is Wales and NI, which I think are not further subdivided, and England is split into South, Midlands and North, with South and North being the best of these. Each region puts on its own championships. There is no qualification for these, or for the Nationals, but you have to be a member of a club to enter. There are hundreds of clubs of different ability.
See
http://www.ukathletics.net
for clubs near where you are thinking of going, then perhaps cross refer to results at
http://www.englishcrosscountry.co.uk
or
http://www.race-results.co.uk
or google a bit to see what standard the clubs nearby are at.
www.athleticsdata.com
is good for looking up results on individuals and you can search by club - but be aware that for the better clubs all the members of a club may not train together, and live all over the country.
Finally, we don't have any of this professional/amateur nonsense, so unless you are thinking of going back to a US college, if you can supplement your student income with race winnings then good luck to you!