FWIW I had exactly the same problem when I lived in Aberdeen. Some corvid carcasses had been found in the vicinity of my house and a wounded crow had been picked up and taken to a nearby vet for treatment some 80 yeards up the road.
The result was an overweight, testosterone-hyped and tooled-up Police Constable banging on my front door 9 O'clock one morning, complete with riot belt, pouches, truncheon, torch, flak jacket/stab vest, webbing and GPMG slung over his shoulder ...... (well, OK, the Gimpy's a fib - but the rest is spot-on) all for a house visit. I was going to ask him where his Humvee was, but thought better of it.
Being generally an upright and (then) a police-supporting citizen, I invited him in for coffee - which he declined - but then proceeded to stand in my kitchen, hands on hips, and grill me about what I owned, where I shot and why I was guilty of murdering an entire murder of crows. The overriding sense was one of assumption of guilt - my guilt. Presumably this was because I owned more than one air rifle and therefore had to be in the fruitcake department.
All I could realistically do was firmly deny his insinuations, as he didn't make any specific threats nor try to seize my equipment. However, when I applied for my FAC some 6 months later and had my initial interview, the FLO who came to my house had full written documentation about 'my' offence, and got quite exercised about it!
It took me nearly 2 months of legal threatening before they agreed to expunge the record. Obviously, the fat and useless plodster who'd bawled me out had written this up as a nice juicy firearms offence, so, be careful.
If I were you, I would write a polite but firm letter to your local senior plod (Sgt/Inspector) pointing out your complete innocence along with your abhorrence of such irresponsible behaviour. This way, if your portable SturmBannFuehrer tries to stitch you up back at the station, you at least have a record of a response and will cast some doubt on his account.
Just my thoughts.