Upvote:3
I haven't tried it myself, but I think you should translate all the relevant medical documentation into English, find your local GP in the UK and talk to them. Regarding transportation of the medicines, I did it before: I used a good thermal flask (e.g. Thermos) filled with ice to keep the temperature low. It did work reasonably well for a few hours.
A hardcore option (which I actually did before): learn how to administer the vaccine yourself (or teach someone who will be around) and just do it yourself. Obviously this is not recommended in countries with good healthcare system like the UK.