3 weeks isn't impossible. I did mine in 3 weeks and 1 day because the day of the GFT was unflyable.
I did mine at Clacton on C152/C172 for navex's but circuit work/general flying was in Supercubs, I went for the tail dragger option as I was looking to get into a syndicate with a Chipmunk and a Tigermoth.
Read your reference material until you know it inside out and everything is clear, on the days when flying isn't advisable, get your exams out of the way.
Any days when flying is possible, grab an instructor and go, I went solo fairly early and did circuits ad nauseum till they let me go on navex's.
I paid 50% up front, 25% half way through and balance after 3 weeks.
I lodged with one of the instructors so that kept costs down and guaranteed me getting there on time every day.
Agree with Whirly and airpolice, you want to become qualified and pay money to do it, it's not complicated - find somewhere that will accommodate you but be prepared to commit yourself fully also.
p.s. Didn't get in the Chippy/Moth syndicate, but ended up in an Auster group which was great fun.