Firstly I'm suprised you need a GP referral, any private treatment I have gone for i have self-referred, referral is usually to get payment authorised from a medical insurer and to prevent hypochondriacs. There is no reason your GP will not refer you if it's standard maternity care however lots make a charge for a referral as this is usually claimed back from a private healthcare provider and to be honest I think it's only fair they do charge for this.
Having had problems in the last few weeks I considered going private - my father is a retired GP and he strongly advised me not to. Be very sure you can go the whole way private or be sure that a quick diversion to private won't prevent you from getting back into the NHS, you can discuss this with your GP but be sure of your facts before you go private. My situation was that after a private scan - which is not recognised by the NHS - I was worried that there was a problem with the baby, after 2 weeks of stress I said if I didn't get it resolved by the midwife I was due to see I would go private - my Dad asked me what I hoped to achieve by that , if they scanned me and decided something was wrong if I wanted back into the NHS I would still have to wait, still have to be scanned again and would have to deal with people who rightly or wrongly would be pretty pissed off with me. If I wanted private treatment what exactly did I expect to happen? Did I know if I could afford it?
If I could afford it I would go private, but I can't. I stuck with the NHS and got there in the end.
I don't know what's driving your choice to go private but talk it through with your GP, there may be alternative courses of action you can take.