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If the conviction was for parking tickets or TV licence evasion, I don't see any reason for it to have any relevance.

But it was for burglary. Would my grandmother, uncle, neighbour or postman feel comfortable dealing with a doctor with a burglary conviction? I doubt it. I very much doubt they would be comfortable handing over or granting access to their most personal and private information to someone with such a conviction, and they should not be expected to feel otherwise.