I was born and raised in the UK and hunted red deer in Scotland on many occasions. My advice would be start at the link below, then find where you want to hunt and contact the estate you choose. Scotland has much to offer over mainland Europe in my opinion, chief among them is they speak English (well, a version of it that is more understandable than a completely foreign language!) and the process to hunt is reasonably straight forward. In addition, the trophies range from OK to outstanding and the people are welcoming. Don't overlook other hunting opportunities while you are there; upland hunting for grouse, pheasant, ducks, geese can easily be provided for much less than you would pay in say North Dakota with no tags, draws or bag limits. About the only things I miss about the UK are my family, the food and the hunting.
http://www.shootinguk.co.uk/shooting/deer-stalking/places-stalk-red-stags-scotland-72515
