What do you mean about not taking injections because of blood clots? The risk to your liver is much greater when you take pills over injections, I've heard injections are relatively safe. Patches or gel would be the other option, I suppose, but I've heard it's easier to get T suppression with monotherapy on injections.
Unfortunately no one I know is rich enough to have gone private, but if you want any tips on DIY + how to get blood tests for free in the UK I'd be happy to help!
Also here is a list of different private options in the UK, there are a lot more than two: https://transactual.org.uk/medical-transition/private-care/