Christ, whatever you do don't step across the threshold of PC World. URghghh.:
Pretty much everything you look for will be running Windows 8. Advantages over Win7 - much faster. Disadvantages - pug ugly, can't find anything, best suited to touch screen which £400 won't swing.
Basically anything with an Intel Core i3/i5/i7 or AMD A4/A6/A8 will give you plenty of grunt. The Intel Pentium is the rebranded Celeron and sucks donkey cock.
A few suggestions:
This one is a small (11.6") screen laptop, with a touch screen, Windows 8, good processor, plenty of disk space. The compromise here is the screen size. Another plus is it's John Lewis, so retail store you can walk in to, and they have a 2-year warranty as opposed to the standard 1 year.
This one is a standard size laptop. It's running the Core i3 chip which is (IMO) better performing than the AMD ones. This is also the 'U' variant of the chip (rather than the 'M' variant). U variants draw half the voltage of M ones, which means less heat produced as a byproduct and means a longer battery life. It has a decent hard disk capacity, 15.6" screen and the manufacturer, Asus, is a good one. In a 2009 laptop reliability survey the top two manufacturers for reliability were Asus and Toshiba. The site, Ebuyer, is a huge tech-selling place although you can't walk in to see them as you could with JL.
This one is £50 over budget but comes with a 3-year next business day onsite warranty. It also comes with Windows 7 preinstalled rather than 8, which makes it less hideous. Misco is also a huge retailer, do lots of stuff in the education and business sectors (business prefers Win7 which is why so much of their stuff is Win7)
Hope that helps.