In the UK you typically go to college (university in our terminology) before you join the Army, rather than after, but we do have bursaries to support some technical specialities if they commit to joining after they graduate. You can also do in-service degrees, up to PhD I believe.
In the US, all officers must be university grads. The enlisted ranks do not need a university degree to join. I would assume the same is true of enlisted ranks in the UK.
Technically you don't need a degree to be an officer in the UK: you only need A Levels (finish high school) to go to Sandhurst and begin officer training. In reality however something like 98% of Sandhurst applicants are university graduates. I don't know the exact percentage of entrants who don't have a degree though, so don't quote me. It has been a while.
P.s. as a famous example, I believe Prince Harry went to Sandhurst without going to university first.
