Thanks. Yes, I'm sure that's the case... let's just say an internet-based sexual offence. Just have to believe that not everyone will be so discriminatory. The actual team that interviewed me are going to be disappointed as they were very complementary about my suitability and experience.

Overnight I've been thinking about how I may get some clarity...
Perhaps, responding with something like:
"I'm disappointed with the decision, but I would like to clarify whether your concerns are around this role and whether I would be successful in applications for other roles within your organisation."

I don't want to waste too much time on it, but obviously it would be helpful to know if I'm just considering a career path that isn't suitable (my research to date hasn't suggested that is the case).

Hi and sorry to hear of your experience. What was the conviction, if you don't mind saying? I think people with certain types of very stigmatised convictions are arbitrarily rejected even if the conviction has zero relevance to the job, unfortunately.

I wasn't asked to disclose at the application stage... the job description said no DBS check (it's a back office admin-type job for a local council).
I was offered an interview and then offered the job (subject to pre-employment checks).

One of those was a disclosure form that clearly stated:
"The Council welcomes applications from ex-offenders and will only consider an applicant’s criminal record where the conviction is relevant to the post. Any information given will be examined by HR and only considered in relation to the particular post for which you are applying." So I was re-assured. 

However they then withdrew the offer stating:
"As the information provided by you regarding your unspent criminal conviction is not satisfactory to [council], I am writing to inform you that this offer of employment is withdrawn with immediate effect."

So, either they are not following their policy, they have certain convictions they always reject or perhaps the way I wrote about the conviction was not 'satisfactory'?

I don't think it's worth challenging, as they're not really going to change their mind and would I really want to work for them after this anyway...?

Any advice on how to avoid this situation in the future though?