If you do need it to be Windows - ie cheap and OK for home use - then I guess you'll be wanting to 'do stuff' on it as well. You probably need office? The Home & Student edition is under £100.
I assume you do not feel confident enough to build your own? You could build a cracking machine within your budget, and while it isn't hard to do - just like lego for grown ups, if somebody gives you a parts list - it isn't for everybody.
Looking at the spec of the machine you linked to... The i5 processor isn't massively expensive, but you could save money with an i3. It looks a little pricey to me, but I suppose you get it all in one delivery.
If you are VERY impatient, you could look to get a Solid State Disk (SSD) as well as a hard disk. I paid about £100 for a 250GB SSD which I installed Windows and Office on. My PC starts up in seconds and Office apps open with a bang.
Dropping to an i3 and 4GB RAM (which is OK) you can get
thisfor £230!
Here's an
ASUS box with a fast AMD processor and 8GB of RAM for £300.
Lots of other options on ebuyer. Also try scan.co.uk.
Of course, with these systems you need a monitor, keyboard and mouse. If there's lots of homework to be done, I'd suggest a 24" HD jobbie... pick up an Acer one for under a hundred quid. Keyboard and mouse are basically free.