It seems that there aren't many places in London to get a Pixel 2 repaired. Google's official route involves sending it overseas, Carphone Warehouse can't say how long it will take to repair and there are only a few independents who can do it. Raphone were able to fix it within a couple of hours. I just booked an appointment on the website and popped in. They were upfront about the process and how much it was going to cost. The phone's as good as new now. Hopefully I won't damage the phone again but if I do, it's good to have found someone I can trust to deal with it for me.