Sure. Check these guys out:
http://www.pcspecialist.co.uk/laptop-computers
Something along the lines of this will do you a good stead - I and a number of others have used the company before and have been very happy with them. my 2011 i5 is still playing games happily today.
5-600 is an odd figure as it plonks you firmly between "decent home" and Gaming spec, but as you've the xbox you don't need to bother with the weight, cost, heat and noise of an integrated NVidia card. Essentially you can get a nice processor, good memory and screen with integrated intel Gfx which will run many things well.
A bit more of a dig puts this together:
http://www.pcspecialist.co.uk/notebooks/ultraNote-15/
Upgrade processor to i5 3340m
Upgrade memory to 8gb
tha-daaaa! �540
If you are re-using windows licences *cough* then take 80 quid off that and maybe look at a faster hdd / ssd, or upgrade it at a later date. 500gb ssd's are on the market for around 250 these days.