Hi Naomi
I can tell you that Gender GP offers a very simple bridging service. It's pretty straight forward to register with them and get monitored access to prescription HRT. All in all, it takes around 4-6 weeks. For most, it's an online service and you are probably unlikely to speak with the Webberleys directly (or at least not very often) but they are readily available by email or by phone in the event of anything more complicated. They are also able to help hook you up with gender therapists and other experts that can help with various aspects of your transition
It's not the cheapest service but it's much safer than going it alone. Initially £195 set up fee and £60 for an information gathering session with a gender therapist. Then you need to provide blood tests - you might be able to get these from your GP otherwise they are around £150 privately. Prescription charges for HRT drugs are quite reasonable starting at around £15 per month but you do also have to pay for the prescription writing and monitoring at £30 per month. Lastly, you have to get blood tests every three months which I believe is around £50 (or your GP might do these for you for free if you are lucky). You might also want to factor in costs for therapy along your journey
Gender GP will also work on a shared care basis with your GP which can be good if you have a supportive GP who is weary about prescribing HRT
From what I've read about GenderCare, their service is more akin to a GIC albeit with a more flexible approach and vastly reduced waiting times. Their approach is on a one-to-one basis from their clinic in London so I guess they would be a bit more confidence inspiring and perhaps better if you aren't quite sure where you want to get to
Neither service should cause you any issues in pursuing NHS services down the line and both will avoid the trauma of a 2 year waiting list to start hormones through one of the GICs
Hope that helps
C x