As a student, I'd think portability was probably essential? I have a mid 2012 13" Macbook Pro which you could probably get on eBay for around £500ish I would imagine, i7 processor, 8GB of RAM, 750GB HDD. I did the upgrades mentioned above and haven't looked back. I replaced the CD Drive with a 2TB HDD in for storage, and replaced the original HDD with an SSD. Works a charm! Upgraded it to 16GB of RAM at the same time. Granted I spent about £350 on the upgrades, but I went with a 1TB SSD and a 2TB HDD which rapidly drove up the price.
To keep the cost down, you could leave the RAM at 8GB for now (I bought my laptop in June 2012, as soon as it was released and only upgraded the RAM last year) and just grab a 128/256GB SSD for it. Replace the internal drive with the SSD and put the old HDD where the CD drive. You can find the parts and tutorials online - I did the upgrades myself in about 20 minutes! As a bonus, you can buy a little optical drive USB enclosure and pop your old CD drive in it so that you don't lose the ability to read or write CDs!
If you shopped about I reckon you could get a top spec laptop for about £600-650. Hope this helps!