The 7x57 will do anything and everything you need, and is a little 'kinder' on roe than the .280 Rem, but not by any huge margin. I stalk in West Sussex and use a 275 Rigby / 7-08 / or a .260 for Roe, Fallow, Muntjac, fox. Unfortunately, I don't have stalking to offer you as all of my activity is undertaken on behalf of a large private estate where there is already a Syndicate in place.
You will need a temporary Firearms Cert BEFORE you arrive in UK or it will be impounded at the place of entry, I would suggest that you decide on the location as the Firearms Certs are issued by the Local Police, which in Sussex is at Lewes. You will find their website at
http://www.sussex.police.uk/advice-and-support/laws-and-licences/firearms.
You could contact Gunrunner at
SPORTING FIREARMS CONSULTANT COURIER SERVICE, Richard Whitely is the man there, and he will have the answers you need both for Sussex and the rest of the UK.
You can expect to pay somewhere around 150 - 200 GBP per day for 2 outings of approx 3 hours apiece, an early morning stalk, and probably evening high seat, with trophy fees on top, which vary considerably from place to place for paid stalking, obviously if it is private ground then that will be between you and the person holding the stalking rights. Richard Whitely has up to date information, I am sure.
Wherever you go, consider security arrangements for the rifle, as not all B & B's will accept firearms on the premises. Maybe the Estate Rifle route is a less onerous route to go?
PM me if you need more info, I might be able to help; but maybe this will give you a starting point.
BTW, Fallow are out of season from end April to August 1st ( Bucks) and until 1st November for Does.
Best
Peter