Very difficult without UK or EU passport or citizenship. Plus UK anaesthetists get paid a lot less even as attending or consultants working in the NHS. At least that's what a UK anaesthetist told me and why he moved to the U.S. even though he had to start all over. Lots of UK physicians Down Under too. Private practice in the UK exists but apparently hard to break into, but I don't know as much about this aspect.
Better if you can go to Australia because anaesthetists get treated well, respected, no CRNA or equivalent threat, not the same medico legal environment so not as worried as in the U.S., etc. Salary not as high as a staff specialist (similar to academic employment), though still higher than UK I believe, but private practice can be very lucrative. Lifestyle much better in general.