Ah - understood on budget.
The TV looks like it would need an HDMI connection from the PC. While some laptops do have HDMI, not that many desktops do, at present.
As for laptops, understood about your concerns, but I would simply plug in (and do!) a full size USB keyboard so apart from one or two functions where the laptop 'function + key' combination might be needed, I don't touch the laptop itself. Hate silly thumb-joystick thing on some models, and not happy with touch-pad, so use a USB optical mouse. Can probably get either item for under a tenner on Ebay.
If you are unlikely to be doing much more than a bit of browsing, using Excel and WP, do you already have access to MS Office for students (as that's going to add 75 ?? quid) ?
Do you have a preference for Windows XP or Windows 7 ? Do you have a copy of (say) Windows XP - just that bigpockets.co.uk has some desktop machines from ~220 pounds where you'd have option to install XP yourself.
Would have suggested something like a Medion or Acer Aspire 'nettop' box. Some have 2 GB RAM, 160 GB hD, wi-fi as standard, and priced below 250 quid. You'd want to add an external CD or DVD, unless you have other machines where you could share an existing drive (for installing software, for example).
I'd have suggested a 25" Hannspree Full HD LCD monitor (195 quid at Ebuyer) which accepts SCART, HDMI and VGA, or an LG which accepts HDMI, VGA, DVI. Alternatively there's an LG display with LED backlighting
www.ebuyer.com/product/177050 Hannspree - 2 mSec response
www.ebuyer.com/product/165285 LG LCD
www.bigpockets.co.uk/ LG LED - model E2250V-PN (VGA, DVI, HDMI) 36 month RTB warranty
With last one you'd need to buy a separate Freeview box.
Hmmmm, sorry for dumping a pile of apparently unwanted odds and ends, but just looking at other options for getting together some value-for-money bits to fit budget...
PS If you don't have XP to hand, I've heard it can be 'downloaded' (wink) if needed. There's a Wiki article about minimum hardware for Windows 7, if you prefer.