i don't know about finding a room in a flat for such a short time but the hostals are pretty cheap, comfortable and central, the cheapest one i've found is about 10 pounds (british) a night. my room in a shared apartment costs 360 euros a month which works out about 8 pounds a night so you wouldn't be losing that much money.
hope this helps,
and, if you need any help while you're here or before you arrive feel free to email me. I'm english and bored!!!