Many of the in service RAF Hawk photos over the years were taken by Geoff Lee, once BAE Kingston's photographer, and if he was the phot on your sortie then it will be easy to obtain copies.
Geoff is famously and deservedly regarded as being one of the nicest men in aviation, and is someone who seems to have managed the difficult feat of achieving professional success while remaining approachable and eager to help people.
He is an absolutely Top bloke!
If it was a service phot, things may be more difficult.
1) It could have been taken at 'Station Level'. If so what happened to the negs will be a complete lottery. They may have been routinely binned even before the station closed, or when the station closed. They may have gone into storage somewhere, they may have been passed on to the RAF Museun (unlikely) or may have been lost.
2) It may have been taken by a Strike Command photographer. If so, Strike might still have the negatives. An approach to their
PR people (Mr Dale Donovan is far and away the most helpful bloke in the department, and the most 'aviation'-minded) might bear fruit.
3) It may have been taken by a DPR photographer (probably Sergeant Rick Brewell at that time). His negatives will be in King Charles St, and may be accessed via the Air Historical Branch, though they're not set up to help private individuals.
Given a bit more detail, or a sight of the picture, I could probably guess which of the above options is most likely.