Here in the western U.S., we're in the middle of our big game season and our native Mule Deer is one of the larger number of game animals taken. Having grown up here, deer is a way of life. I imagine most Brits would find it a little 'gamey' since our equally native sagebrush is frequently browsed by the deer and lends a definitive flavor. Mule deer are fairly large, with a two year old buck weighing maybe 100 pounds field dressed.
At any rate, deer meat has little fat... in fact any fat is on the surface of some cuts and little or no marbling is present. This demands a method of preparation recognizing the finished product can be a little dry (hence tough) if not cooked properly.
Our favorite method is to take either the steaks (cut from high on the hip) or chops (cut from the backbone) and soak them in buttermilk for maybe 15 minutes and then dredge in salt and peppered flour at least twice. During the dredging, a cast iron skillet is brought to a medium high temperature with perhaps 1/2 inch of lard melted. The lard adds a pleasant flavor not imparted by vegetable oil. The steaks are a little thinner than seen with beef... maybe a maximum of 1 inch.
Browned on one side takes maybe 3 to 5 minutes and that's repeated on the off side.
Here, the favorite sides would be simply prepared.. baked Idaho potatoes served with sour cream and butter and a cold, fresh lettuce/tomato/onion salad. Add home canned green beans, et voila!