Going into halls? Check what they have. My university did have contents cover with Endsleigh for halls, for an extra £6. It covered all non-mobile contents (i.e. not mobiles, laptops, tablets) but it did cover desktop computers.
If it's private - i've just done it with Endsleigh again actually. As above, extras need to be added on for portable devices (phones, laptops, tablets, cameras) and extra for things like instruments, bikes etc. but basic cover can be something like £25 (that was based on about ~£4000 contents cover). I went through this over the phone with them, as there's a few odd bits and pieces with the online one - don't get tricked into something more expensive.
Cover4Students I believe is the other alternative, although not used them myself. I couldn't find much other than those two.