I had a very similar situation at the beginning of my PPL(A) course. I had 20hrs from my RAF Flying Scholarship but had a log book provided by the school and signed off by the CFI and his number at the back. According to the CAA it can only count for up to 10hrs of your total PPL(A) time. So, if you can provide them with the proof, you'll only have to do a min of 35hrs.