You can build a moderately cheap PC only if you can recycle things like your case, dvd drive, maybe...MAYBE your hard drives.
I built a new one in November for Skyrim and I paid a little over $500. I bought one new hard drive but recycled by old ones and my case. Everything else I bought was new. New proc, memory, video card, DVD drive, motherboard, power supply.
The most expensive part in my new build was the GeForce 560 2gig OC (it's not even the Ti) and that was around $320. I guess in total I spent closer to $6-700 but still. I came close to my original budget.
All these prices are USD.
EDIT*
I'm running Skyrim on Ultra settings with my current build.
Also, the op has the best user name EVAR!
Cheers for the info, and thanks haha, only 2 people have got the ref so far
For building your PC, just check http://www.youtube.com/watch?v=lPIXAtNGGCw.
I'd say 600 pounds would be appropriate to run Skyrim at high settings with little to no lag. Anything above that will make the game look even better, with possibility of graphical mods and with no lag at all.
Cheers again, looks promising
Thing is you have a computer and you have a 360 anyway so instead of buying a new but poor PC and a next gen console (I'm assuming you might) pool the money together and build a powerful PC instead. You can then update it bit by bit over the next years when you want/need to and then you have the best of both worlds.
Maybe you can save money on a screen by hooking it up to your TV (if that is a possibility) at the end of my bed. I have mine hooked up to my 32 inch TV and playing Skyrim is pretty awesome.
Also because you can use a 360 control you can still leisurely lay back and relax if you want to. Also with it being hooked up to your TV you are saving room.
My PC cost me around £800 when I put it together, it would have cost about £1000 if I had it pre built due to the mark up so make sure to build it personally.
You can save money also by reusing your older mouse and keyboard because frankly any old set will be perfect for example
This is the GPU I have http://www.amazon.co.uk/012-P3-1573-KR-Nvidia-SuperClocked-320-Bit-Graphics/dp/B004S6Z0FM/ref=sr_1_4?ie=UTF8&qid=1334001488&sr=8-4, very nice, very powerful and when I got it it was about £330 so there are some bargains out there
Cheers to you too! And thanks a whole lot to everyone else who's contributed, this is looking pretty promising actually.