This is the laptop I'm talking about, it seems to have everything apart from a good graphics card. I guess they're integrated graphics, but since Minecraft isn't really a game that demands graphics I wondered if it would be okay for running it at high settings? (Full render distance, Fancy graphics etc)
http://www.refurbthat.com/reconditioned-laptops/lenovo-thinkpad-t410-2522-core-i5-m540-2-4ghz-4gb-memory-320gb-hdd-dvd-rw-with-windows-7-professional
Added (1). If I do buy it I will be upgrading the RAM to 8GB and the Hard Drive to 500GB.
Added (2). Okay if that one isn't good enough please check out this one and tell me if it is any better
http://www.refurbthat.com/lenovo-t510-intel-core-i7-2-67ghz-4g-memory-320gb-hdd-dvd-rw-with-windows-7-professional
Added (3). If none of them are good enough can you please see if you can find a good laptop for me? I don't have a lot of money so a price of around £400 or under would be good. As I said, I will be pretty much just playing Minecraft on here.