For most people, it's just not going to be worth it. There are almost always good public transport links between halls / uni / town, as so many people use that route. Of course, if you have placements then things may be different.
If you're part of a sports team that travels a long distance for fixtures, then it can be useful (people will chip in money for petrol), but it's not really a reason for taking one. Arguably, it's a reason for not taking one, because it means you have to drive for hours when knackered.
Although my own uni lets you buy a parking permit for halls, regardless of special circumstances e.g. disability. However, it costs about £125, there's not really any parking on campus / in town is pay & display only, congestion is horrific, and other services (e.g. big Sainsburys) are pretty much on your doorstep anyway. And a bus pass costs £185 for the year - much cheaper! TBH, often the fastest way to get around big cities is by bike - it lets you dodge all the congestion.
With regards to the unis that you're looking at, Cambridge is quite compact, so you won't really need to get in a car to go anywhere. If you want to get around that bit faster, then I'd suggest that there's a reason why cycling is so popular in Cambridge - it's as flat as a pancake. UCL and Imperial are both in central London, so between the congestion charge, congestion, lack of parking and the easy availability of good public transport, it's just not going to be worth it. I don't know anything about Sheffield, but Loughborough is a campus uni, a bit of a way out of town (although the bus links are decent), so this is probably only uni where a car would actually be useful.