The paperwork you are given at the visa medical in London is fairly good. I was asked to sign the following statement. They offered to give all the vaccinations I needed then. I refused as I thought I had given them more than enough money that day. However, I wish I had just done it there and then.
" Although vaccinations are not required for my K visa application, I understand that they will be required when I adjust status to that of legal permanent residency following marriage. I understand that I may, depending on the US state, have to partake in a medical when adjusting if I elect not to be vaccinated at my UK medical appointment."