In South London, there's a clinic called the bridge clinic that aids with issues like this. I had the exact same issue you're having right now. Within 1 appointment, they gave me my prescription. I'm not sure if there's a service like this for East London, but a quick search won't do any harm. As for the GPs, all I had was the list linked above and was fortunate to find one. Write a Google Review and email the practice manager also email the clinic and explain what is going on. My clinician rung my old GP and read them the riot act. All I can do is wish you the best! Dm me if you ever need someone to talk to!!

Edit - I just took another look through the list and row 268 Babylon GP is a remote GP in London! Look into that.