You will pay by the hour. They will normally want some money up front (if so expect a discount).The PPL is a minimum of 45 hours, you may well require more hours if you need extra training. You will also have to pay fuel surcharge etc per hour. You will also have 2 hours for your test and the CAA test fee. If you fail or get a partial pass there is another fee to pay and aircraft hire again.
Also PPL written exam fee's.
Also accomodation & flights & food etc. CAA licence issue fee's.
If you do your PPL in US, remember you will need a few hours in the UK to get up to speed. more fee's!
If you are going to get the fATPL, then I would advise doing your ATPL written exams after the PPL. The advantage of this is, it allows you to do your hour building just before you go onto do your CPL and IR, therefore you are current and can practise. Rather than doing your hour building and then sitting in a classroom for 6 months!
Don't forget your RT exam. If doing PPL in US, Its my opinion that you do this back in the UK with a good school. Oh yes, don't forget the RT fee & CAA issue fee.
Basically everything has a fee!! and normally a big one!
Also if going abroad to do a PPL check what the weather will be like when you are there! For a PPL allow no less than 4 weeks.
Enjoy it.