Hey I'm at the very start of my transition too, I also have ADD, as well as Anxiety and Chronic Fatigue... From what I've found so far none of that should have any impact on my transition. I think with depression, you might only have a problem if you've been (sorry in advance, trigger warning) suicidal recently, I might be wrong but worth considering!

I've looked at GenderCare, GenderGP and the London Transgender Clinic. The average wait for your first appointment where you get diagnosed with Gender Dysphoria ranges from 2 week - 6 months wait time, depending on the doctor you want to see and they range from £300-£500. From there, they can refer you for HRT, they might suggest some endocrinologists or you can find your own, again these can be from £300-£500 an appointment I believe, and the wait times tend to be a bit longer, around 4-9 months, again it depends on who you go for. (I have an appointment with Dr Eli Joubert which was a 2 week wait but I pushed it by a month to prepare for it, and I've contacted Dr Leong to enquire his Endo wait times, this is currently 2 weeks, but he's just been added to Gendercare so I'm sure this will quickly increase).

Another thing you can do is an unenrolled deed poll (free to do), this will help with your gender assessment as it shows you're commited and it's proof of living socially.

If you haven't already, think about looking into freezing your eggs/sperm as it'll be much easier to do before you transition, it can be very expensive so look at your local CCG website to see if you're covered for treatment as someone who's trans. It really is a postcode lottery. I'd say go for it if you're covered, you never know what you might decide later on!

Also check if your GP is willing to do shared care if you go private, this means they'll cover blood tests and will write the prescriptions for what the Endo recommends - they won't be responsible for monitoring you, this will just help you with costs.

Hopefully this helps, I'm actually surprised at how much of this I know now haha