If a conviction is 'spent' under the terms of the Rehabilitation of Offenders Act, you do not need to disclose it to a potential employer (with a very few exceptions that do not include airlines). If the conviction is not 'spent', you will need to disclose it, but driving offences are very unlikely to compromise your chances of getting a flying job. They will have absolutely no effect on your airside pass application.
If you were applying for a job as a bus driver or similar, it would be different. But you aren't.
Scroggs