Most universities have a minimum of 3/4 sides, so whatever your ability you'd be able to get into a team and play against other universities sides. I.e. If you got in the 3rd XI in your first year, you'd play other Universities 3rd/4th XI. It doesn't matter if you're a 1st or a 3rd year, if you're good enough, you'll get into a team after the trials.
If you're a fresher, you're highly unlikely to get in to Uni 1st teams or UCCE teams, (UCCE teams will be the top university teams in the country who play against major counties in pre-season warm up games), but one of my friends has just got into the Loughborough UCCE side in his 3rd year, so it is possible. Then again, he does play minor counties cricket, so you've gotta be pretty decent to go this far!