As others have posted, it's a difficult one to call but you should apply and be totally open and honest when filling in all the paperwork and if asked at the interview.
If your prospective employer (NATS or whoever it may subsequently be) is willing to employ you, then their support as a reputable employer should be enough to satisfy the airport authority security protocols.
Additionally, as an ATCO, your airside pass would probably be very restrictive in terms of going anywhere but the ATC complex and the manouvering area (if at all).
Fraud is fraud but it sounds as if you were on the lower edgeof the scale, there are Atcos out there who've done worse things.
Just be honest and if asked, ensure that you show a suitable level of contriteness for your moment of madness in the past.
The latest "informed sources" say that Fidgell is being banished to the land of Safeskys at Her Majety's Pleasure.