I thought you could have your PPL training on a Private C of A aircraft or a PFA aircraft if you were the sole owner (or husband & wife)?
Regarding the comment about navaids for the skills test, how do you get around that if you are doing you PPL in a Tiger Moth for example? Do you have to do that bit in a suitably equipped aircraft or are there alternative nav tasks you can perform?
PS It wasn't called a Skills Test when I did my PPL and navaid training had to wait until the IMC Rating