Flying hours usually count provided they they are certified correct by the school where they were flown. On application for a PPL the school has to certify that you have completed all of the mandatory training, if they are not sure what you have done, they will only certify what training they have given you!
Yes it is possible to do a PPL in 21 days but not to be recommended. Ideally about 6 weeks is the optimum time for absorbing all the necessary material. Those who learn quickly usually forget equally as quickly! Schools that offer a 45 hours PPL in 21 days provide you with exactly that, a 21 day PPL; there is no guarantee you will be any good or anything better than just about safe enough to get a licence. if you then wait several months before you fly again you'l probably need another 15 20 hours to convince a school to let you hire their aeroplanes!
The UK average hours to get a PPL is arround 55/60 in North America its actually higher!