I was able when coming back to UK to have a notarised translation of a local criminal record certificate for the countries worked in before returning, translated by a professional.
Depending on the country, this can be surprisingly cheap. Both countries are wanting to join the EU (this was when the UK was a member) and the Embassies in London were happy to help in the event of any questions.
It was about 7 years between re-joining Easy and leaving for my current company, so the same problems didn't exist. A standard 'Basic' check and letter from the company were enough for the (EU) country I'm resident in now when we moved, even post-Brexit. I'd worked for this company at a UK base for around 5 months on base transfer.