You'll need to speak to your University SU Sports/Society officer to organise setting one up. Although to do so you need to have at least 10 people comitted and ready to pay and start straight away. You'll also need to have a full plan including finances, training, tournaments etc....
Although you may have to settle with being registered as a University Society. For it to be a sport, it has to be on the official BUCS league, which needs at least 8 individual universities to register, which the UK doesn't quite have. We potentially could, but there's not really much point in a way, just because the travelling involved to move teams to home/away fixtures (unless the whole league was done at bricket wood or something...), so using NSPL/CPPL/KOTH/SUPER5s is a lot easier
Even if you get lucky and the uni accepts it, my team's funding falls short of about £250 a year. :/ In the last 2 years all we've acquired are some Ion XEs and 5 bunkers :/ it's a long slow process unless you're willing to heavily invest yourself as my team has.
Despite this, there are several universities with paintball teams (although not all of these may be active)
Portsmouth, Leicester and my squad (University of Gloucestershire) all competed in Proto's KOTH league last season
There's also Southampton (i think have one), Birmingham, Plymouth, London City Uni, lancaster. So there are plenty out there, it's just a case of being able to organise them all...