I have a lot of experience with the UK mental health system (through myself, my mother, and several other members of my family) and I'm going to give you an annoying answer....it depends on which psychiatrist you talk to....and it greatly helps to have one with experience treating trans patients.
What is "supposed" to happen is that they need to determine whether or not your issues are causing your GID. Now it seems common sense that a large proportion of trans people have anxiety and depression BECAUSE they have GID and that transitioning would help.
I'm not sure that makes sense so I'm going to try and summarize it

If they believe your anxiety and depression are causing your GID, they will want to "cure" the former before even looking at the latter
If they believe your GID is causing your depression and anxiety, then you're good to go
If they believe your GID and depression/anxiety are totally separate to one another...then things may get complicated. They may want to tackle both at the same time, which might include various types of meds on top of taking T or it may just involve continuing to see someone to talk about how things are going. Or they could decide they want to tackle one thing at a time - a psychiatrist not familiar with trans people is more likely to opt for tackling the things they are more familiar with.
Now CAMHS specifically...I'm not 100% sure...I've only been on the "adult" side of things. From what I've read though it seems really hard to get T if you're under 18, regardless of mental health issues - so I can only assume that having mental health issues and being under 18 is going to make it harder. It's certainly not impossible because I've seen it happen but I don't know how they did it.