I'm in the uk too and I agree that 6 sessions or even 20 sessions is very sub optimal to help or treat Depression (for most people imo )

I think there may be a "cultural problem" and more stigma over here

I hope you are able to work things out. It can be a bit dicey over here as well. Both my pdoc and tdoc stopped taking my insurance and I'm having to pay them out of pocket. It gets expensive. Good luck.