The police are aware of this problem and try to mitigate that risk.
The best solution is to ask them to give you the ‘other lawful quarry’ (OLQ) condition, which was recommended for general use by ACPO in June 2009.
Whilst badgers are not normally a lawful quarry they become one to anybody who has the relevant licence from English Nature.
In my view OLQ should be the standard condition applied to almost all FAC for live quarry shooting.
Essentially once you have established a good reason for shooting one quarry species OLQ allows you to shoot any other if your circumstances subsequently change.