I don't think I can quite fit a 1055t in. How about an AMD Phenom II X4 955 Black Edition Socket AM3 3.2 GHz 8MB L3 Cache Retail Boxed Processor instead? It will most likely do better in games and its £30 cheaper, putting within the budget.
Although if I'm getting a black edition processor I'd best learn how to overclock...
New spec
Be Quiet 530W Pure Power PSU - 120mm Fan Dual 12V Rails 5x SATA 2x PCI-E £48.99
Gigabyte GA-870A-UD3 870 Socket AM3 8 Channel Audio ATX Motherboard £83.64
Corsair 4GB (2x2GB) DDR3 1333MHz Memory Kit Unbuffered CL9 £75.03
LiteOn IHAS124-19 24x DVD±RW DL & RAM SATA - OEM Black £14.80
Samsung SpinPoint F3 500GB Hard Drive SATAII 7200rpm 16MB Cache - OEM £34.98
AMD Phenom II X4 955 Black Edition Socket AM3 3.2 GHz 8MB L3 Cache Retail Boxed Processor £127.63
Coolermaster HAF922 Windowed Version bundled with FREE Coolermaster TX3 CPU Cooler £84.99
GTX 260 - £84
Comes out at about £550. £20 over the top end of his budget, but he'll live . I'll just give him the extra 20 or something.
I should google that free cooler...