I am a Special Constable and military researcher who looks up details of servicemen on the National Records for medal research purposes. However,Special constables medals are difficult as they are not published in the London Gazette as servicemen/MBE/OBE holders are, and your G/Dad would have been locally recruited in his respective county. What I suggest is that you approach the constabulary in writing through the Special co ordinator and ask with full details as full name DOB and what station etc as desk diaries were kept. I hope you do well. Do you hold his long service medal?