ads678 – depends on your interpretation of the relevant laws. Wildlife and countryside act S11(2) covers other species and specifically for deer the Deer Act 1991. Most people, imho, interpret the deer act incorrectly, though it depends on where the deer ends up. If you hit it and it remains on the highway I consider it fair game; if it ends up a few metres from the highway it would likely be an illegal act to remove the carcass.
With the wildlife and countryside act; if you accelerated or swerved, for example to hit a pheasant, you would be deemed as being in immediate pursuit of the animal, this is a criminal offence. If it is a genuine accident; you are unlikely to be deemed as being in immediate pursuit and therefore collecting the carcass would likely not be an offence, imho.
Though I warn you; I recall a story/rural myth from when I lived on the west coast someone picking up a warm deer carcass and putting it into the back of his car, antlers and all, unfortunately it was not dead just knocked out, it came round in the car and trashed the interior.