Sam,
I applied in February this year and just received my course allocation in mid September. It takes a good 5-6 months to get through the 3 stages, online tests and medical (although I've had to have extra reports sent). My advice would be apply with about 3-4 months of your course left to go at Uni. I was in my final year as well and taking 2 days off to go for Stage 2 and Stage 3 isn't an ideal situation if you have dissertations and other deadlines to hit. I've also found that some gentle prodding is sometimes needed to get NATS/CAA to reply to things, or to find "lost paperwork".