Not that I know of, and I am a developer who has actually read and tweaked the code for the Clock Applet before. It looks like the items are sorted in descending order of current time in each location, then sorted by the name of each location (in the event that two locations in the list have the same local times, like Birmingham and Tunis in your list).
What I'm saying is that no matter what order in which you add the locations, the locations will always appear in the order displayed above.
I'm not necessarily going to commit to changing the code for you, but if you ask enough, I might get up off my (loaded-down) posterior and write a patch for this -- for you. I'd try to contribute it "upstream" afterward, and chances are that'd work, but the official "upstream" changes are going to take a while to filter down into Ubuntu MATE officially. Therefore, in the meantime you'll have to run through steps much like those described in this post of mine: How to modify and rebuild a package for Ubuntu MATE (or Ubuntu, or Debian)