Few questions about seeing a private GP in UK?

Hi, i want to have some hormone tests done which i can't get through nhs but funds are limited. The tests are very common: Testosterone, Estradiol As far as i'm aware you pay around £30 for the appointment, does the doctor have to agree these tests are necessary or can you pay for them even if the doctor doesn't agree. And if it is found that there is an abnormality where treatment is needed will i have to pay to follow it up. Also if i see a private GP will i no longer be under my current surgery? Thanks.