Docash - I think they tend to be fairly open-minded. Most people who I've met at selection days have been in their early 20s and either not long out of uni or still there. Given the entry requirements (good A-levels) and bearing in mind that most people who get good A-levels will then go on to university, I would have thought that they expect a large number of current students to apply. I can't speak for them, of course, but it would seem logical.
Don't let the fact you're still at university put you off applying, but I certainly wouldn't apply if you're not in your final year unless you intend to drop out if you pass selection (but then this might not necessarily look good if you're asked about it in an interview.) As an example, I applied in December last year and had completed the four stages and class 1 medical by the end of March. I had a five-week wait between stages 2 and 3, which is much longer than some people, so if you're considering applying with the intention of finishing your degree first I would personally suggest doing so in January or February of the year you intend to go, and then see what happens. As NickS said, it is possible for them to accept your initial application and then put you on hold, depending on what you specified as your first available date on your application form.
And thanks for the best wishes... I can't wait to get going! Leaving for LHR in a couple of hours...
Edit to say: Pilot37 - given the high pass rate at Stage 4 and what the course can offer if you do pass, are you really going to pack it in at this stage? Many applicants would give a hell of a lot to be in that position. Not a criticism, just curious.