I'm NOT saying that this is what I'd personally recommend - but going with your MINIMUM COST approach, this is the cheapest I could find on OCUk
Funnily enough - about the £280 mark that you mentioned!!
Intel Pentium 4 805 Dual Core "LGA775 Smithfield" 2.6GHz (533FSB) - Retail (CP-116-IN)
£73.95 (£86.89 Including VAT at 17.5%)
Asus P5VDC-MX VIA P4M800 Pro Micro ATX (Socket LGA775) Motherboard (MB-137-AS)
Price: £36.95 (£43.42 Including VAT at 17.5%)
2x OcUK Value 512MB PC3200 184pin DDR Memory (MY-002-OK)
2x Price: £22.95 (£26.97 Including VAT at 17.5%)
Maxtor DiamondMax Plus 8 40GB 6K040L0 ATA-133 2MB Cache - OEM (HD-085-MD)
Price: £23.50 (£27.61 Including VAT at 17.5%)
NEC ND3550 16x16 DVD±RW Dual Layer ReWriter (Black) - OEM (CD-035-NE)
Price: £19.95 (£23.44 Including VAT at 17.5%)
OcUK Value Rainbow Series Case Silver With 350W PSU (CA-000-RB)
Price: £19.95 (£23.44 Including VAT at 17.5%)
Total INC VAT = £258.74
I really just was interested how cheap you could do this - so I took it very litterally - I've not even looked it over properly - so there could easily be a fundamental mistake in my suggestion
/edit - changed mobo for inbuilt graphics.....