The attack happened at around 3pm last Monday (the 8th of April).
The three men were described as being in their 20s, with skinheads and wearing tracksuits - and the vehicle as a blue/grey type of estate car wich was thought to have one or more of its hub caps missing.
PC Simon Tibbett said:
"This was a despicable crime that led to a badger dying in a very painful and cruel way and we will not tolerate wild animals being treated in this manner.
"I am appealing to anyone who has not yet spoken to police about this incident and witnessed it to get in touch.
"I'd like to speak to anyone who knows whether the badger was alive or dead before the men took it into the woods and I'd also like to hear from anyone who recognises the car or men from the description given."
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The attacker grabbed her dog lead wrapped it round her neck and started to strangle her before running away.