From CAA point of view, no problem. We often have training paid for by people other than the student (teenagers come to mind!)
From the flying school point of view, we might need to keep a record for money-laundering purposes if the total exceeds Euro15k or a series of transaction might lead to that or a few other things.
https://www.gov.uk/guidance/money-la...sponsibilities
For HMRC, then you are best to have a chat with an accountant, or look to a tax forum, rather than a flying one!
ps. There used to be a scheme where you saved tax on training for a CPL, the first part of which was gaining a PPL. Of course, many people stopped their CPL training shortly after completing their PPL ;-)