100% legal to humanely dispatch any wounded/injured animal by any humane means possible weather it is protected or not or in/out of season.
Did it with a doe before wrapped around a sheep fence with a broken hind leg. There was no hope of getting the leg out it and you couldn't walk away and leave it, infection was already set in and there was a lot of blood lost. The leg had to be cut from the fence in the end.
Took pics before hand as proof and I knew the below bit existed before doing so.
(7) Notwithstanding subsection (5) of this section, it shall not be an offence for a person—
(a) while engaged in agriculture, fishing or forestry, or in zoology or in any other scientific pursuit, unintentionally to injure or kill a protected wild animal, or
(b) while so engaged to interfere with or destroy the breeding place of such an animal, or
(c) while constructing a road or while carrying on any archaeological operation, building operation or work of engineering construction, or while constructing or carrying on such other operation or work as may be prescribed, to kill or injure such an animal or to destroy or injure the breeding place of such an animal, or
(d) to capture an injured or disabled protected wild animal for the purpose of killing it humanely or with the intention of tending it and of later releasing it, or
(e) to kill humanely a protected wild animal which is either injured in the manner described in paragraph (a) of this subsection or captured in the manner described in paragraph (d) of this subsection, or so to kill a protected wild animal injured in the circumstances described in paragraph (c) of this subsection,