Desktop is fine as you'll probably be able to find a uni computer for more powerful programs, the portability of having a powerful laptop is definitely worth it though if you can find a cheap, smallish, i7 x700hq powered laptop or what you'll find is better value for money is getting a laptop with a GTX 1060 in it as it'll give you the best of both worlds and cost a similar amount to an equivalent GTX 1060 PC + monitor + a chromebook while still being able to play games on a similar level to your PC as long as you're not going above 1440p (so it works out better unless you're playing at 4k then fair enough as 1070 and 1080 laptops come with a bit of a premium).
edit: actually if you do computer science you should be able to get a free copy of windows 10 as your department will have an agreement with microsoft, I've forgotten what it's called, but yeah taking that into account you could get a custom GTX 1070 laptop for that kind of money as well actually, or a 1060 for ~£1100.