Obtaining a PPL in the 4 weeks in the UK is possible but it requires a certain amount of luck, I did my PPL at welshpool last summer and it initially looked as if I may complete it in 4 weeks but then it took about 5wks waiting around to do my qualifying cross country which I'm sure has been a stumbling block for many. I got there in the end butwe're all at the mercy of the British weather. Anyway good luck and if pool aviation are still around I'd definately consider them.