I can show funds totalling well above £10k pounds (500k PLN)
If you mean 10,000 pounds, then that's 50,000 PLN, but yes, even that would be enough.
As for the bank not stamping things, you could open a Polish bank account and put the bulk of your funds there. They'll stamp a bank statement for you. You could open a PLN account and a separate foreign currency account and leave most of your sterling in that, get statements for both and get them stamped.