Easy to say "Don't pay any landing fees".
In the real world most/lots of places are charging for each landing and T & G in the UK.
Anyway back to the question!
Kiev23:- Due to your location and recent posts all the airfields/airports in the North west of England charge for training landings and t & g.
The number required for you to become proficient at landing a light aircraft and completing the course in your budget will depend mainly on you! Continuity of your lessons and effort seem to be the key.
Weather conditions and your instructor (do you get on with them) are also factors.
I would say you could do a JAR PPL (A) with a total of 100 landings at your base airport. As I said above add more if you have poor continuty etc. etc.
Good luck with your PPL.