pi4t: Speaking as a current (UK) student, I went down the gaming-desktop-and-cheap-laptop route (in fact, I took the latter to extremes and was given the laptop for free, but that's another story). The desktop fits fine in my room; I've had it either on top of or to the side of my desk, depending on the configuration of my room in a given year. If the university (or other accommodation provider) is particularly stingy with respect to space or desk size your daughter may have issues (particularly if she also wants to do handwritten work on the desk). Hopefully you'll have had a chance to see the rooms at open days by this point, though, so you should be aware if that's an issue. If the university doesn't offer accommodation (for the full degree), then...I have no firsthand experience with private providers (yet) since my college has offered it for all four of my years. But I imagine that at worst it would mean rejecting one or two options for not having a big enough desk.
The bigger issue for me has been transporting the desktop to and from university. I don't live too far away so my family has come up to collect me and my stuff at the end of term, but it's still meant it's had to be carried up and down flights of stairs and installed in its locations and home or in college six times a year. Earlier this year (my fourth) the fan started coming loose and I had to get it replaced. Not a major issue - it only cost me about £10, though I didn't dare use the desktop until it was fixed - but annoying and it could end up being more serious.
If you're planning on having your daughter use public transport to bring her things to and from her university at the end of term, a desktop will be more of a problem - you don't want to have something that big to take with you, and it won't enjoy the trips either. The only solution I can see there would be for her to manage with just the cheap laptop while at home, and leave the desktop at the university. And that relies on the university either not letting out the room to other tenants during the holidays, or offering a safe place to store valuables - and that's something you should definitely check, particularly if it's a more famous/touristy university.
Also, you're very generous buying a gaming computer for your daughter - I had to buy mine myself!
Thanks, this is exactly the I'm-living-that-life info I was looking for. Most universities here only make you completely clean out your room over the summer term (you can leave all your things in your room over Thanksgiving, Christmas, & spring break, even if you aren't allowed to stay in your room over break), so it should only be a case of moving the desktop once or twice a year. All of the schools we're considering are only 45 minutes-2.5 hours away, and we expect to drive her or have her drive herself at term end, so she won't be lugging it on a bus or train.