When I went to work in the Falklands, having yellow fever injections and a load of others was in the contract, this is not unusual, there was also a requirement to declare any time in prison.
It seems after so many years people under UK law don't have to declare a prison sentence, but Falklands law mean anyone who had been given more than 6 months were not allowed into the country, and no time limit.
So during the building of airport we had an arsonist, and the FI police asked UK police if any of the people working on airport were known arsonists, the UK sent the records of all people asked for, not just arsonists, and we had around 200 workers who had to be repatriated.
This caused a problem, as contract signed in UK, but included working abroad, so the worker had given false information by saying he had not been to prison, so the company could sack them, but under British law it was permitted to withhold that information.
So this leaves employers with a problem, they must tell people like care home owners of the risk, but they don't know the risk, so having all employees vaccinated makes sense, but there are a few people who due to under lying medical conditions should not have the vaccine, so we hit the disability laws. So some medical examiner has to state that some one has some problem which prevents him having the vaccine, and as a result awards them with a % disability, at which point the employer can't insist the person has the vaccine.
If you have ever needed to go to a tribunal to get a disability recognised you will know how hard this is. But it would seem the firm can require one to have vaccinations, and have been doing that for a very long time, and I have all the paperwork for my vaccinations in my old Passport it is nothing new.