Ok now that it is morning and I don't have Sam breathing down my neck to get off the computer I can reply properly.
As I understand it your NHS and ours are quite similar in that the worst cases can be treated for free under public funding so long as you don't mind waiting. In saying this anybody can go private at any time but it will need to be payed for.
The first thing you should do just to get the ball rolling is to go back to your doc and get all the prelim tests out of the way so you don't have to do them once you finally get to see a fertility specialist (waiting list is months). If I could do it again I would be so much more pushy with my GP because now I know I wasted months and months because she didn't think it was important.
All of these tests will be payed for publicly except the doctors visit itself.
Hey you may get pregnant this month, you never know or there may be something wrong that will need to be fixed before it will work. Being told to wait another 6 months sounds stupid to me!!! when he could just do some easy blood and semin tests to see whats going on.
Skip ahead months and months until you finally get an appointment with a specialist.
(This is why I say start tests now because your GP can't refer you until one months blood work and a SA are done then you go on the waiting list and wait)
I'm not exactly sure what the criteria is in the UK but here they have a points system to see if you quality for treatment. There are a couple things that are no goes. Like you will not get treatment if you smoke or if you are over a bmi of 30 and a few other things then they rank you to see how much you need there help getting points for things like PCOS or blocked tubes or length of time you have been trying and if your points are over a certain threshold then you are eligible for public funding.
We unfortunately found nothing wrong with us that they could see and because we have Madelyn we wont qualify for public funding for IVF or IUI for another 3 years.

Our fertility doc then suggested that clomid may be a good option to try first privately as it is only $50 (nz) (26 pound) per month which covers the blood test analysis twice a month and the drugs.
Hopefully that is what you were wanting to know I went a little over the top but meeeh oh well
I hope you have a great day
BTW 9DPO today!!!!!! not long to wait now. My boobs are killer sore again this month.