A conviction which is 'spent' under the rehabilitation of offenders act does not need to be declared for a flying job, nor will it turn up on the basic disclosure which is required for an airside pass. That is why they are called spent convictions and that is why it is called the rehabilitation of offenders act.
Whether they would hire you before it is spent I don't know, but if some overworked recruiter is going through a pile of CVs and there are 49 without and 1 with a criminal criminal record, what do you think is gong to happen?
It seems to me your best bet is to plan your training so you finish around the time your conviction is spent and start in the aviation world clean.
You could of course try CB1's suggestion and see what turns up. A basic disclosure costs £13.60 + £0.50 bank costs if you pay by card.
Good luck.
Gerard