This is not qualified legal advice my reply is from background knowledge and online research
For any job, companies can ask your permission to apply for a DBS (Disclosure and Barring Service) check during the application process that will show any criminal convictions. Enhanced DBS will also show police cautions.
It all depends how old you were when you committed the offence and were convicted. The sentence that you received matters as that determines when the conviction will be 'spent'. If the conviction is spent but you need a Standard DBS or an Enhanced DBS you might want to be honest include how you made reparation or addressed any underlying behaviour you had at the time. For sensitive employment postings needing enhanced DBS they may look at the risk element here and you could be declined employment. This particularly applies to work with children or vulnerable adults.
Basic DBS checks will not usually include 'spent' convictions (but some serious offences are never 'spent')
Standard and enhanced DBS checks will I believe show all spent convictions, even minor convictions, so you may experience some difficulty if you wanted to work in the below listed jobs. Some Forces jobs might show leniency for applicants with a minor assault conviction but as far as I know definitely not for dishonesty
-Jobs that involve working with children or vulnerable adults -Senior roles in banking or finance -Law enforcement roles, including the police and judiciary -The military, navy and air force -Work involving national security -Certain roles in healthcare, pharmacy and the law -Certain roles in the prison service -Private security work
There are a couple of link details below that explain the filtering process for convictions and table to show age and sentence versus the 'spent after' time required. There are also legal companies who can advise you (for a fee I am sure) Failing that Citizens Advice could assist you or just make a generalised search on admissibility under the web page of the job you were applying for?