I won't be able to continue with private care after the initial consultation, so how to I go about transferring back to the NHS for follow-up care?
This does happen but it is considered very poor practice, both from a jumping the queue perspective, but also consultant using their private practice to benefit them. Some consultants do get away with it because it is not made known to the Clinical Commissioning Group, but if it is, they could make the decision that this can't happen. Some CCGs have already put policies in place to stop this practice and private hospitals (who often do NHS work too) know better than to challenge.
Saying that, your suggestion of keeping your NHS appointment is fine, but you can't be guaranteed that you will see the same consultant or that he/she could consider the information gathered from your first appointment.
The benefit of it really depends on the reason to go private. If it is for an outpatient appointment and then an MRI/ultrasound for instance and you are prepared for the latter, than it might be worth it. If it is outpatient and then cheap medication, then again, that's fine. However, if it is to start a process that you suspect will require follow-up, then don't expect that the process will be sped up by jumping the clue. If it is to get prescribe medication but then expect that this will be available on the NHS, it is highly likely that won't happen until you see the NHS consultant.
My OH has suggested at time that I go private, but for the above reasons, I've always said it was pointless. Saying that, you can ask to go ANYWHERE for an outpatient appointment, so you could do your research and if you're prepared to travel, ask where you could go. You might be able to contact a commissioner to and ask for advice, they might be aware of providers they commission from with shorter waits.