Ok, this suggestion made me look up the possibilities. There are no races in Edinburgh while I'll be there. I found one in London. Based on the number of entrants in last year's race, there is a distinct possibility I would finish last. Also, overall, not that many entrants - under 100 last year. I'm considering it, but really, do I want to spend a good part of one of my days in London figuring out how to get to Victoria Park on the Underground, taking the Underground in my running clothes, running the race where I will be among the slowest out there, and returning on the Underground in my sweaty running clothes? Not really.
Given the number of races I found in the whole of the UK in my google search - running 5k races doesn't seem to be quite the past time over there that it is here.