Its more about peace of mind. When you buy a console, there is no longer any worry or thought about upgrading or 'can I play this?' or anything like that. You buy the console and that's it. You're set and you can totally forget about specs and tweaking and whatnot. Its much simpler.
Not to mention that if you buy a console early in its life, its gonna be pretty powerful and comparable with a decent PC in terms of what sort of graphics you'll be getting.
http://uk.pcpartpicker.com/
This place factors in shipping into the costs of the products, so the final price is what you pay. It also tells you about an compatibility issues and uses multiple product sources to always find you the best deal. Sticking with *just* Amazon or something might get you free shipping, but you'll probably spend more in the end due to not shopping around.
Here's a build with everything you'd need for less than 750 pounds:
http://uk.pcpartpicker.com/p/1fxdN
This would play most current games. Also keep in mind this includes everything. Monitor, operating system, keyboard/mouse and speakers. If you have some of these already, you can cut some on the price and perhaps upgrade something else(in this case, probably best to go to an i5 processor for better future-proofing).