That's not how you should value consoles vs pc's. Very few people have PC's only to run it as a console replacement with prettier graphics, they get used as PC's as well. You have to add at least £300 or so to the budget of the desktop to account for the fact you're getting a (bleeding quick) pc in the bundle as well as the gaming grunt.
If you're looking at just a console beater with no other use for it then it'll basically be a steambox linux machine which could be cheaper, but kind of missing the point of PC gaming tbh.
Anything from a 660Ti or 7950 up should really show the consoles what's what for the most part, and if you want to go that route it only costs about £550 or so with a decent AMD CPU.
But I prefer looking at your overall purchase price:
Console c. £400
Games x6 (that's conservative but better to work at the minimum point to prove the point): £240
Boggo standard laptop for fb, work etc.: £350
Xbox Live/PS+ subscription: £30
Total: £1020
PC with 7950, AMD 8320 etc. roughly £550
Games x6 (let's say they're the same games, so still expensive but cheaper than consoles i.e. leaving out the fact that there are awesome cheap PC staples like CS:GO, TF2, League of Legends, Planetside etc.): £120
Don't need to buy a boggo laptop to cover work because you have a desktop: £0
Decent peripherals: £50
Total: £720
If you'd need a laptop regardless of having a desktop then the budget becomes a bit closer run but you've got to look at all a gaming pc offers beyond the pure gaming grunt of a console. The pc budget still has plenty of room for another monitor, speakers etc. without pushing the costs of console gaming.
What a load of drivel. The OP has set a budget of £680, the cheaper the better, for a gaming PC to better an Xboxone. So, what laptops and the cost of games have to do with this, is beyond me.