Deer Act 1991

The Deer Act provides for the hunting of deer and so regulates how, and it what manner, deer may be taken. As such, it also includes provisions for rehabilitation and/or euthanasia:

Deer Act 1991 Section 6, General exceptions:

(2) A person shall not be guilty of an offence under section 2 or section 3 above by reason of any act done for the purpose of preventing
  the suffering of an injured or diseased deer.