Bearcat, in the past, Brits et al have gone to the Caribbean to fly. Just as some Aussies have gone to the Pacific Islands to fly too.
It's hard work finding the opportunity, but what I would do is find out where in the world "scenic" flights take place. Then do the research to find out what the operators want. Then see if your qualifications and visas match (or can get close to it).
yes, the world has changed and it will continue to change. With the internet and a few handy search words, you can find out a lot.
As for the FBOs? No, you don't need a CPL to be a dispatcher in the UK/Europe. Just keen and a willingness to learn and crack on. Best way to get a job at an FBO, once again, the internet is your friend.
Where do most bizjets operate? Look up the directories and see if you can find them. It is getting increasingly more difficult to get onto the airfields these days.