I built a system at work the other week for £165 (inc VAT)

It had:
AMD Sempron 64 3000+ (Skt 754)
Asus K8V-VM
512MB PC3200 DDR400 Memory
80GB Seagate SATA Hard Drive
Cheap black and silver case with 400W PSU
Sony DVD-ROM Drive
Onboard Video and Sound
Add on a cheap 17" LCD for about £90, Windows XP Home SP2 for £65, keyboard, mouse and speakers for £30 and you have an entire system for the grand total of £350. Was very nippy when I installed XP Pro on it as well and was still nice and responsive when I had finished installing all the programs
EDIT: You could even stick Vista Home Premium on it for an extra £10 and add in a £30 PCI-E graphics card to allow her to use the aero interface and you'd still be under budget