Along with REPS there are plenty of other organisations that have set up lists/registers of personal trainers. The NRPT is the most well known.
The only thing to note is that unlike the REPS the NRPT is a privately run non governmental organisation that charges trainers to be on the register (around £100 per annum) and so is a profit making organisation. They do though have the widest list of qualified and insured personal trainers not just for the Thames Valley and London (where we cover) but for the whole of the UK. They are also the best ranked register if you are looking for a personal trainer in London.