Totally agree with you. And you didn't break the law. You gave her your details! Its for her insurance company to find out who insures you!
Law says ...
If you have an accident that causes damage or injury to any other person, vehicle, animal or property, you must give both your own and the vehicle owner's name and address, along with the registration number of the vehicle, to anyone having reasonable grounds for requiring them. (this has to be on a public highway, which includes supermarket car parks or any place to which the public would generally have access)
If you don't give your details then you should report the accident to the police as soon as possible within 24 hours.
You must also report the accident to your insurer, even if you're not intending to make a claim.
If you fail to comply with that, then technically you are breaking the law. And just to clear it up, the bit about animals does not include ALL animals like squirrels, it only includes.
Mules, Pig, Dogs, Sheep, Horse, Ass, Goat, Cattle
Thats the law, i'm not saying i always follow it, but its helpful to know it.
Alan