To be trained for a licence you need a qualified instructor who has to operate within a Registered Facility (RF). Yes, the instructor does log the hours because the instructor is the captain of the aeroplane. Why would an Instructor wish to pay for your training; when the instructor has probably had to pay 4-6 times more than your PPL to qualify as an instructor?
There are two ways to reduce the cost:
a. find somewhere where the cost of operating an aeroplane is substantially less i.e. overseas. Always look for hidden costs such as landing fees, not all airfields add them to your bill!
b. Apply for one of the scholarships that are available e.g. Air League