I would go with the AMD solution over the Intels, they're better for gaming (if that's what you want to do) and most other tasks, the only area Intel chips are slightly better at is video encoding, otherwise they have been proven time and time again to not be as good (check out Tom's CPU chart comparison on the tomshardware.com front page - you can compare processors at different tasks).
£400...mmm...well roughly looking over www.overclockers.co.uk you can get:
> CP-121-AM AMD Athlon 64 3700+ San Diego 90nm (Socket 939) - Retail (ADA3700BNBOX) (CP-121-AM) - £135.95
> MY-041-CS Corsair 1GB DDR Value Select PC3200 CAS2.5 Kit (2x512MB) (VS1GBKIT400) (MY-041-CS) - £51.95
> MB-053-MS MSI K8N Neo4-F nForce4 (Socket 939) PCI-Express Motherboard (MB-053-MS) - £57.95
> GX-101-SP Sapphire ATI Radeon X800 GTO² 256MB DDR3 TV-Out/DVI (PCI-Express) - Retail (GX-101-SP) - £117.95
VAT £63.67 Total £427.47
That setup should give you fairly good performance in most games today with a view to be able to play some nice games in the future. Other stuff (office, browsing etc) should be a breeze also. THe GTO2 version of the X800 can also be modded with a very high success rate (althought it voids the warranty) to an X850 XT (and some have clocked it to PE speeds!). Making a 140 quid card become more like a 250 pound card.
I think moving to dual core with this budget will force your to cut down on the graphics card, something that if you want to play games is not worth doing. The 3700+ is a fast processor for the money.
If you can find a cheap one and are keen on overclocking, try to get an Opteron 144 (1.8Ghz, Socket 939). They overclock incredibly well (2.8Ghz - 3Ghz!! Higher than an FX-57!) and have been able to be had for less than 100 quid, but this will need decent cooling and powersupply etc. But bang for buck they're amazing.
Ok just to let the US people know, get 400 pounds, * ~1.8 for the ratio, then half it for the price difference in the UK. Seriously guys, its expensive over here. So Imagine he has around $350.
I have an X2, never looked back. P4s run a little hot for my liking.
You can get cheap RAM in quite a few places - overclockers.co.uk do 2x1GB sticks for about 130 quid. (Despite the US being able to get the same sort of stuff for about $200.)
Mobo's I'm not hot on - I run an Asus A8N-E, X2 4400, 2GB Samsung 3-3-3-8 RAM, Radeon X800XL from pcspecialist.co.uk. I got a complete system, came to more than double your budget (with HDDs, case, PSU etc.)
But the guy above me has some nifty info (I just posted, read his comment, and edited this one )
I would not touch a p4 you will get a lot more performance for your money with AMD.
If gaming is your priority then I would go with a single core.
Dual cores are good but you will be paying a lot more for them and unless you want to multitask its not worth it IMHO at the moment if your on a tight budget.
I guess you are not an overclocker (so I will not recommend an opteron) but may want to in the future so I would suggest these:
AMD A64 3700+ £155 Here or AMD (Venice) Athlon 64Bit 3200+ £113 Here
Abit KN8 Ultra SKT939 NF4 £66.51 Here
I would have recomended the AN8 ultra but its discontinued. Some one might recommend a better motherboard for the price as I have only ever dealt with Abit and Asus.
PowerColor ATI Radeon X850 XT 256MB GDDR3 £165 Here
If you want to save money you can buy the x800gto2 and unlock the pipes and overclock it to take it to a x850xtpe for £135 Here
You could drop down to 1gb of ram but IMHO programmes are starting to use more and having 2x1gb in the long run is better than say 4x512mb.
You will find ebuyer and overclockers will beat each other on price for different things but if you use both you will be hit with expensive delivery charges.