I've just bought one for my daughter, who's off to university next month. I'd recommend looking at manufacturer-refurbished models (often ex-demo) rather than buying new, as you'll get much more for your money that way. I paid just over £400 for a laptop that I'd have expected to pay between £550 and £600 for new. There are plenty of refurbished machines on eBay and Amazon.
The highest priorities for her were weight and battery life. She'll be lugging this around all her classes, so she needs it to be light (and slim) and not to need to be plugged in during the day. Universities usually won't allow students to plug in devices to charge in teaching rooms in case other students trip over the cables.
Most students will store stuff in the cloud, and the university will provide a fair amount of free storage, so hard disc capacity probably isn't all that important. Many newer laptop/notebook computers don't have hard discs at all: they use solid state device (SSD) storage, much like built-in high-capacity memory cards. So RAM (I'd go for a minimum of 8 Gb but ideally more), cache (maybe 2 Mb), processor speed (over 2.5 MHz) and number of processor cores (4 is pretty standard, I think) are more important.
If games are important, it's worth looking for laptops with dedicated graphics cards (e.g. NVIDIA or AMD Radeon), as these will provide higher-quality graphics and usually make the games run more quickly. They do push the price up, though. I think it's useful to have an optical (DVD) drive to run old games, install other software from DVD and make physical back-ups of files. Most cheaper laptops - and quite a lot of more expensive ones - won't have this, so you'll need to see whether your son thinks it's important.
Anyone with an ac.uk e-mail address can get massive discounts on Microsoft Office software, even if the university doesn't provide it free. They can also get discounts on things like Spotify Premium, which is important to most young people, I believe.
All new computers come with pre-installed anti-virus software. This will be free for the first 6 months (usually) but will then become very expensive. The first thing I do with every computer I buy is delete this and install a free anti-virus programme (Avast is my preferred one) and an anti-spyware/malware programme (sorry, I've forgotten the name of the one I have on my laptop at present). I think the university will probably provide a security package, in which case these things can be deleted when he gets there. Also, avoid installing any "recommended" add-ons (browser toolbars, etc.) as these will slow down the computer significantly.