Including display, and other peripherals?
Or are we just talking for the PC build, easily doable I'd say.
An integrated motherboard ION or AMD Fusion is around £100 or less.
whatever mini-itx case floats your boat plus PSU, say up to £75?
PCI-E 1x DVB-T cards are available at a reasonable price if you shop around, call it £40?
DVD drive for around £10
You install the OS to a usb flash drive if you want but a 2.5" HDD is also good, say another £40.
£265 so far.
TBH though depending what you want, and where you shop it could be less. My build done recently is:
Thermaltake Element Q - £50.38
beQuiet 300W SFX PSU - £38.76 (due to wierd compatability issues with the included Thermaltake PSU)
GA-E350N - £48.02
Xenta card reader (with IR sensor) - £3.99
Windows Media Center Remote (from ebay) - £10
DVD drive - £12
Total -- £165 (obviously plus a bit for shipping from a couple of shops)
So far no problems for me, though i've only been using it a couple of weeks. Plays all my DVDs and AVI rips no problem.