Without wanting to sound in any way flippant, my immediate reaction to that question is to say "a doubling of the budget"
Video editing, if it is to be at all professional in nature, requires a specially-configured computer, and really good machines of this type don't come cheap. You'll see quite a few computers that profess to be 'basic video-editing' machines, but frankly many of them aren't worth buying.
Video work stations can cost several thousand pounds, but it is possible to get one that is capaple of decent results for a good deal less than that. Having said that, I doubt that you'll find anything worthwhile under £900/1000. Certain makers tend to specialise in these machines, and if money is tight I suggest you take a look at this click here
Laptops are out as far as your budget is concerned, so you're looking at a tower. Here are a few basic tips:-
1. get plenty of RAM - you'll need it - and certainly don't settle for anything less than 1024Mb.
2. Big hard drive capacities are a must - 300Gb would definitely be my start point. Preferably go for two drives, one for Windows, and one for the video files, and make them fast - a fast hard drive is absolutely critical if you're at all serious about video editing.
3. Be choosy when it comes to your video editing card. You'll see three main contenders in this ring - Matrox, Pinnacle, and Canopus. My personal advice is to forget about Canopus, I've heard stories of major customer-service problems, and software/hardware incompatibility issues.
It's a complex subject, this, and there isn't room here for a comprehensive guide - no doubt other forum members will have their own recommendations.