No, you shouldn't worry, just keep at it.
A lot of us are overqualified from qualifications and experience in our home country. Unfortunately the British like those qualifications to be from the UK. We all find something eventually so just keep at it. I applied to dozens and dozens of jobs I was qualified/over qualified for (and that paid a lot less than my last job in the US, which was aggressively average pay for management level there) and only was ever offered three interviews. One was actually the job I have now.
All you can do is expand your search parameters. Maybe that means in terms of location, or type of work, but when you get your foot in the door things will be a lot easier. It just takes time and patience. Get someone to look over your CV and cover letter to make sure you're presenting them the way a British employer would expect to see them.