OP, in relation to gun/knife crime/crime in general. Every city in the UK has it's problems with crime; much of this crime is against people who don't use their common sense. If you're going to walk alone down dark alleys drunk at 2 in the morning then you need to expect to run into trouble. If you apply some common sense and keep in groups on well lit streets then the chances are that you'll be very unlucky to get involved in a knife attack. At the end of the day, you could easily get involved in a knife attack or similar in Leeds or Guildford so its not as though "If i go to Nottingham, i will get stabbed, if i go to Leeds i definitely won't". So i would personally forget about crime rates and focus on the uni and city as a whole.
Personally i think that Nottingham is a better uni than Leeds or Surrey; this is overall, i know that Surrey has a pretty good reputation for your subject though.
You need to know whether you want to be in a city, a large town or a campus on the outside of a large city.
With Leeds, the uni is bang in the centre pretty much; it's know as a student city and you have Leeds Met uni as well as Leeds Uni so there are loads of students and lots of student deals, pubs, clubs etc.
Surrey is in Guildford, which is a large town; i've never been there so don't really know much about it; what i do know is that i wouldn't even be considering Surrey. Worse uni, small city; not for me personally; but then i am going to London for uni so im biased towards larger cities.
Nottingham is a decent size city and its a campus uni about 5 miles from the city; its near the town of beeston though so its got everything you need in walking distance. I won't bother saying anything else cause you have opinions on Notts already.
Overall, i would go for Nottingham though; or Leeds if you prefer a really studenty city and the crime rate of Notts bothers you.