Have you every considered how much would it cost to stay in Warsaw for one month and what is the cheapest place to stay? I think if you wish to stay in Warsaw for a month to be on the safe side and be fully covered you have 2000 English pound notes with you, many people have survived on much less and have enjoyed their stay in Warsaw.
Why Struggle for pennies?
I'm a strong believer in always being in credit and having more money rather than less. I would suggest you find a local paper in Warsaw and put an advert that your looking for cheap place to stay for one month, I'd also state you can pay in cash upfront. If your serious about exploring this neck of the woods or any other here in Poland this is one way way amongst many.