Was this with Leeds? They didn't go into gender stuff because they'd already found a reason to exclude you before they got that far.
That telephone consultation is something they started doing a while back: it's a screening call and its purpose is to try to make their waiting list as short as possible. It's worked, too: Leeds' waiting list was 4 years as of last year; now it's down to 2 years... mainly because they're weeding out people who don't push hard enough. They're getting rid of patients who aren't desperate for GIC treatment; they'll only see you if you're a good candidate who seems to have a clear-cut case of Gender Dysphoria.
The calls start with your mental and physical health, because that's one of the main areas on which they can exclude potential patients. So if you have any mental illnesses - including depression and anxiety - they will expect these to be well managed before they see you because you need to be mentally stable before being seen by gender services. But if as you say you're already in treatment, then those conditions should not present a barrier to you and they shouldn't be able to exclude you for them. They'll only move onto gender stuff if they're happy that your mental health is either good or well-managed, and for some reason the call handler thought yours wasn't, so they didn't move onto the next section.
Another problem may be that you expressed uncertainty about whether hormones etc. will be right for you. The staff member who calls you isn't a doctor - they're more likely a nurse or similar - so they can only assess clear-cut cases of Gender Dysphoria, not the more subtle cases such as yours. So that means they can't be sure from the phone consultation that you have Gender Dysphoria. Of course they fobbed you off: the NHS as a whole - not just Gender Services - is all about fobbing off as many people as possible so that only the truly desperate get seen.

So... what to do now? you have a couple of options:
- If this has just happened today, call them back and ask to speak to a supervisor. Tell them you think the call wasn't handled correctly and explain where you think they went wrong. If you do this quickly enough, you might be able to correct the mistake & stop a letter from being sent to your GP... and you may be able to save your place on the waiting list. If a supervisor isn't available, call the hospital's PALS service and ask them to intervene.
- If you find it easier to get your point across in person rather than over the phone, ask for the screening appointment to be done in person, with a different staff member. Not everyone can use the phone (I can't for example) so they have to make face-to-face appointments available.
- Once you have their refusal in writing, immediately lodge a written complaint (contact the hospital's PALS service for details on how to do this), detailing all the points that you believe to be incorrect. Their refusal letter will also go to your GP so make sure you discuss it with your GP too, and ask whether your GP would be willing to complain on your behalf alongside your complaint. A letter from your GP (once again) explaining the treatment you're receiving will go a long way.
- If all else fails, ask your GP to refer you to a different GIC. If you're in the Leeds area, Sheffield is your nearest bet - although you are entitled to go to any GIC in England, irrespective of geography.
The current waiting times for a first appointment are:
Newcastle: 13 months
Daventry: 24 months
Nottingham: 24 months
Charing Cross: 14 months
Laurels, Exeter: 14 months
Sheffield: 16 months
Leeds: 24 months
So if I were you, I'd start by ringing back & asking to speak to a supervisor; then lodging a written complaint; then if that fails, get your GP to refer you elsewhere. Definitely mention that the assessor misunderstood your mental health status and disregarded the evidence you've already provided them that you're being treated for it.
Good luck!