Novatech Elite N1540 cost £589.98, that is abit more than your 500£.
That one in terms of gaming would be really good, it has decent GPU, and not so bad CPU.
SSD would make it fast so no problem turning it on/off while on class.
Novatech nFinity N1404. Not so good GPU, but still great. It costs £494.99.
With that one you would be able to play most games, but dont expect ultra.
Its not heavy and not big, so better for uni.
My choice is Novatech nFinity N1404 if you are more casual gamer and want lap mostly for uni.
If you are hardcore gamer, and not really uni geek, go for Novatech Elite N1540.