The answer to the US prices being lower is probably in several parts:
1) Utilisation.
In Arizona I saw them do a good five 1hr flights per day, 360 days a year. That's most of the way to TBO every year. The airframe manual was full of 100hr checks... The instructors don't seem to mind, either - despite being somewhat knackered at times
One can't do much about the weather here in the UK but I have never seen a school do what I would describe as half decent marketing, aimed at people who can actually afford to fly.
2) Parts.
Here in the UK, the average small item is probably double the cost v. the USA. I have not had significant bills for airframe parts myself but have seen comparative avionics costs, and here one certainly pays 2x as much. The US distis are banned (by Garmin etc) from selling direct overseas, which protects the revenue of the European distis, who in turn look after the margins of the UK avionics fitters. And, on the old planes that nearly all training outfits around the world operate, there is a constant stream of parts to replace.
3) CAA maintenance
Without a doubt the CAA 50hr check is a significant cost. When I was on G-reg this added about £10/hr (inc VAT) to my direct costs, and that was a new plane, with very little remedial work. The 150hr check added another £10/hr. Whereas in FAA-land, the 100hr check (comparable to the CAA 150hr one; both are similar to the Annual, on most types) isn't necessary for self fly hire; it is required only if one is training other people in the plane. I don't know how many US schools take advantage of this, but it does mean that if a plane is approaching the 100hr mark, and they have enough planes for their training requirements, the aforementioned one can be set aside for self fly hire only.
4) Leaning
Not sure how widespread this is but it was routine to lean in cruise in the US. My UK training experience is that it was
never done. This adds best part of £10/hr to a PA28. I know UK schools prefer people to fly full rich because the engine runs cooler etc etc (& all the old arguments about leaning etc etc) but the end result of the UK training scene routinely flying full-rich is that the wet rate gets inflated throughout the industry by this much, and everybody pays for it.