If you do have a criminal record, it would depend very much on the type of offence you committed. If you got done for lifting a tin of salmon from Tesco ten years ago, they might let it go, but running packages for terrorist organisations may give them cause to reconsider your employment in that job.
If you do have a criminal record, though, then it's best to say so up front. If you say you haven't and they find out you have, they'll just add dishonesty to the list of reasons for not employing you.