I think something like
this might fit the bill. They're not flashy, but the price is right and they're well reviewed. Certainly better than either the Logitech or Bose speakers mentioned previously. While these don't come with a subwoofer, they are a genuine two way design, which means the highs aren't artificially boosted. Later, when your budget allows, you could add a subwoofer to improve the bass.
Here's a professional review.
Or
these, only slightly more expensive, a similar deign but with a larger cabinet, so the bass is probably a little better.
But check eBay, there are tons of inexpensive speakers in the London area, and if you can find a set that's not too far away, that might be your best bet. For example, check out
this auction for a pair of Wharfedale Linton 3 XPs for £40. The cosmetics aren't the greatest, and you'll need a separate amp, but they're complete, and they're probably way better than any of the new speakers already mentioned.
