It's up to you. In Southampton certainly, you can generally find computers around, though I must admit the department computers were a lot better than the ones in the general university computer labs/library.
Most people nowadays have laptops, I'd say, they were certainly useful as you can take them anywhere, and wireless internet is pretty much standard across campuses. Having said that, if you wanted to run autocad, whilst most laptops nowadays are up to it, nothing beats a twin screen desktop for heavy duty engineering or programming. They're also cheaper for gaming.
My laptop went with me to some lectures, the library once or twice in 4 years, it was used on the train home, and at weekends where we went away with societies - a cheap netbook would have sufficed though. I used my desktop more for engineering work - but even this wasn't very often - the software packages we needed were available quickly on department computers, and were generally set up correctly, so I used them, out of convenience.
You could theoretically manage your degree without a computer using university systems and resources, so just pick whatever suits you. A gaming (Skyrim - high, etc) laptop can be had brand new for £650, a gaming desktop is probably cheaper. It's up to you.