As you quoted in £'s I am assuming you are in the UK. You may want to look into something like this:
Simple plug and play USB speakers that are well within budget and should be ample for a small bedroom and reasonable listening levels. If you wanted to spend a little more look into a USB audio device and active monitors from the same site, I have used them before and have found them to be both knowledgeable and helpful. Also may want to look into DV247.com as a potential source, they are mainly London based but you would also be able to visit and test most likely if you give them a call in advance.
Consider 5" drivers as a minimum with possible sub, or increase the driver size to 8" and forget the sub. Be aware that a sub can cause vibration in OTHER ROOMs of your house if not well located. I used to have a sub on a bedroom floor with wooden floorboards, the room downstairs had a nice rumble even at low listening levels.
I would recommend auditioning and purchasing locally over a blind internet buy