In terms of the airline saying 'no'; I don't know.
In terms of gaining an airside pass; well, I followed the link to Disclosure Scotland provided by Scroggs in his first post. This is turn links to a page at the Department of Transport
(clicky) which outlines the offences that would disqualify an applicant from obtaining an airside pass.
It would seem that the DfT set the criteria by which the issuance of an airside pass would be refused and they are not issued at the discretion of individual aiport security teams. As an example, a motoring conviction for speeding does not appear to preclude the issue of an airside pass.