Best Answer
The person who ran int the bank of you is deemed as being 100% liable under rules that deem this type of crash to be what is called strict liability.
What this means is that vehicles following behind are required to leave sufficient room allowing them to stop in the distance they can see to be clear. They are also required at a speed that is appropriate for the conditions which ties in with the safe distance requirement.
The only way the third party can apportion some of the blame is if it can be proved that you brake tested them or braked for no apparent reason.
It is accepted that emergency braking for a large animal running out in front of you is reasonable.
So don't worry, it is down to the car behind, just notify your insurers and get the letter of claim sent.