The only checks that would reveal old convictions are the enhanced checks. The enhanced checks are only for jobs dealing with the vulnerable in a position of trust.
Even for an enhanced DBS, it's at the discretion of the police to omit some items.
I've mentioned this tragic story before: Driven to suicide as a result of an enhanced DBS certificate – the problem with the disclosure of police intelligence
[X] got the job and was told that she would need an enhanced Disclosure and Barring Service check. [She was allowed to start work as long as she applied for it immediately.]
Several weeks later her DBS certificate arrived and on it, disclosed under the ‘additional information’ section was her Penalty Notice for Disorder (PND) for a public order offence. [X] had received this whilst she was at university and on a night out with three of her fellow students...[X] had a strange feeling [men they passed] might be undercover police officers so jokingly as she walked past them, she made a pig-like noise.
One of them grabbed [X's] arm and told her that she had committed a public order offence by ‘making a pig-like noise in the vicinity of a police officer.’ They told her that if she accepted a Penalty Notice for Disorder (PND) and a fine she would avoid having to go to court. Believing that this was her best option, [X] accepted the PND.
[X] thought that was the end of the matter but of course as her enhanced DBS certificate was to show it most certainly was not. When she took the document to her employer, they told her that she’d acted dishonestly in not disclosing the PND and she was instantly dismissed.
You know the rest from the title of the report.
www.the-record.org.uk/unlock-people-with-convictions/driven-to-suicide-as-a-result-of-an-enhanced-dbs-certificate/
You can appeal against the disclosure of some information so it doesn't appear on an EDBS: hub.unlock.org.uk/knowledgebase/local-police-information-2/