Yes OP, you can ask in certain situations for certain jobs.
There is a huge difference in potential employers in small businesses WANTING to know and actually having the right - legally or morally to know.
Obviously I can only go on the OP saying this employer does not want to employ ANYONE with a conviction. So they're not taking any of the information in context - they are disregarding someone on the basis of them having a conviction. They don't care what/why/how it happened.
And that does go against the rehabilitation of offenders act. I am probably biased as know many ex - offenders who I would trust above other non - offenders I know.
In the absence of possible risk to vulnerable people, every one should be judged on their merits, their ability to do the job and the person they are now.
Because otherwise we're saying that anyone with a criminal conviction should possibly be excluded from most jobs.
And the absence of a criminal record is no real indicator that the person hasn't committed previous offences or doesn't pose a potential risk.
Thousands of offenders don't get caught and don't get convicted every year. In my experience, the people I worked with in MH who posed the most risk to the public had no previous convictions. A history of violence/sexual offending yes. But no convictions.