Hi there,
I love the .375 and feel that it is very appropriate for red deer, especially the ones that we have here in lowland England, which can be absolute monsters when compared with their Highland cousins.
Recoil is really not too bad, over a short range session. I shoot a Blaser .375 which weighs about the same as a Twiglet but find it very manageable, with the Blaser recoil reducer in place.
There are only really three downsides:
(1) Trajectory, which is not quite as flat as, say, a 30-06, a possible problem in the hills, but not in the woods
(2) The Plod. According to their guidance notes, .375 should be approved primarily for African use and this might prove a problem, depending on the attitude of your local force. I believe, however, that it is possible to approve an African rifle for UK deer once the African trip is over.
(3) Energy limits on MOD ranges, which will require special procedure for any reasonably stompy calibre.
James