Dear Sam,
It was great to hear from you! Choosing a laptop can be confusing, so here's what I'd recommend after helping lots of friends do the same.
First, think about what's most important. For university, you need good battery life, because you'll often be away from a plug in lectures, so look for at least eight hours. It should also be light enough to carry around all day, ideally under 1.5 kilograms. A comfortable keyboard matters too, since you'll be typing a lot, and 8 GB of memory is the minimum you need to stop it slowing down. Unless you're studying design, you don't need an expensive graphics card.
As for where to buy, I'd check online shops like Amazon or the manufacturers' own websites first, because they usually have better prices. Many companies also offer student discounts, so ask about those.
A good laptop for study costs around 600 to 800 pounds. You may find a decent one for under 500 pounds if you wait for the September sales, so don't rush.
Let me know if you need anything else!
Take care,
Luke