It is always possible to find a digital/FPGA job in UK. Maybe it is a bit difficult at the moment.
I have seen many of the companies working on FPGA advertised job for a year long. And they couldn't get someone to fill in. I guess some of them, they are not really looking for new employee.
Watch out with the job agent as well. They are big sharks.
Two things are the most important:
1) Experience with latest technologies (at least 5 years....)
2) Working visa if you are not local