This is interesting. www.quittance.co.uk/help-article/when-is-it-safe-to-emergency-stop-for-an-animal
"Should you perform an emergency stop for a dog?
Many road users (and dog lovers) would argue yes. However, if you slam your brakes on to avoid hitting a dog, you may present a danger to other road users.
The car behind might crash into the back of your car, which could cause injury or damage to either vehicle, and raises issues around who is responsible.
The driver who performed the emergency stop may be at fault, if they failed to check that it was safe to do so. Equally, the person in the car behind could be to blame for not driving at a safe distance.
The issue with emergency stops is that the situations when they are required rarely leave you time to consider the options, and people usually act on instinct. If you have been involved in a collision caused by emergency stopping to avoid hitting an animal, your case will be considered on its own individual facts.
The Court will look at reasonableness; for example, was the animal large enough to cause damage to the vehicle or injury to its passengers?"
So no, legally, unless there is absolutely no chance of damage or injury to your car and passengers, and those around you, you shouldn't legally just perform an emergency stop.
Morally, most people try and avoid hitting anything. Even stupid pigeons. No-one drives at them with the intent of pigeon slaughter, but it's idiotic, dangerous and probably illegal to prioritise their well-being over that of everything else on the road.