Sadly, there are a few practitioners at some NHS clinics who have bad reputations, particularly with disabled patients. And some of the clinics are better than others.
However, there are many of us who have successfully transitioned on the NHS, including disabled people with complex needs who are aided by support workers. It's more difficult, but it is definitely doable. You've said before that you're under the care of mental health services and you have support workers... and both of those things can make some clinicians extra-cautious. Have you asked to see someone different at the GIC? It could be something as simple as a personality clash that's getting in your way. You have the right to ask to not see that particular woman & to be assigned to someone else.
Alternatively, you have the right to attend any GIC in England, not just your nearest one. If you're not getting the service you need at your current GIC, you can ask your GP to re-refer you to one of the others. There are several, including London, Sheffield, Leeds, Newcastle, Northampton (Daventry), Nottingham and Exeter.
Some, such as The Laurels, are much more proactive and I know that the Clinical Director of The Laurels is pushing to have both breast augmentation and FFS routinely funded on the NHS for trans women who want these procedures. So why not try somewhere else? You could get on the waiting list now (Daventry and Exeter have the shortest lists at the moment) so by the time you get to that point, you should be able to at least get surgery on the NHS and save yourself a small fortune.
Also, bear in mind that the reputable private doctors who prescribe hormones will expect you to come back for follow-up appointments - each of which will cost you extra.