As far as I'm aware, if you choose to see a Consultant as a private patient, then all the subsequent follow up appointments, investigations and treatments have to be done privately too. Is your wife being seen privately for her maternity care? Who decided to send her to the gynaecologist? Usually if your GP refers you to a consultant, or for investigations, you can choose to go public or private, whether you have health insurance or not.
In the past, a lot of people were jumping public waiting lists by seeing a Consultant privately (with minimal delay) then being put onto a public waiting list. Whereas there was a long delay for the public out patient appointments. It is not possible to do this anymore.