I think you might really struggle to build what you suggest for the budget you quote.
Prices here are very competitive click here
Have a good look.........but to give you an idea.
Cheapes Core2 Duo £140 click here
Cheapes motherboard to put it on,just under £40 click here
1GB DDR2 533 RAM £73 click here
Bottom line graphics card capable of playing modern games well £109 click here
300GB SATA hard drive £62 click here
19" TFT monitor £143 click here
Case with adequate psu £55 click here
DVD/CD writer £23 click here
Decent keyboard/mouse £30 click here
That lot comes in at £675 and doesn't include things like a floppy drive or any software (like Windows for example)
It's an Idea of the cheapest,lowest spec Core2 Duo rig you could build that still uses decent components where needed.
You could cut a few more corners that might get you a copy of XP Home oem for the £675 in my example.
If it was me I would be wanting to spend a couple of hundred pounds more in order to get more storage,more memory,an additional DVD ROM drive and maybe the next model up Core2 Duo cpu.