Preheat the oven to 140°C (120°C fan oven) Gas Mark 1. In a big frying pan, heat the oil then briefly brown the sausages. Transfer them to a deep, lipped baking dish along with the venison chunks, then sprinkle over the flour, thyme and pepper. Mix well to coat everything evenly in the flour.
Put the mushrooms, chestnuts, stock and port in the frying pan and bring the liquid to the boil. As soon as it starts bubbling, tip all over the meat and give everything a good mix. Cover tightly with a double sheet of foil and put in the oven. Bake for 2 ½ hours.
When the meat is done, taste the gravy for seasoning – it may need some salt, and stir in the cranberry sauce. If you want to bake straight away, top with the pastry now, if you’re getting ready in advance, wait until the meat is completely cold before adding the pastry top (and then keep the pie chilled for up to a day before baking, or freeze for up to a month).
Dampen the lip of the baking dish with some water. Unroll the pastry sheet and roll it out a little thinner, if you need it to be bigger, then lift carefully onto the pie. Trim off the excess by running a sharp knife along the edge of the baking dish. Brush the top with beaten egg, then scatter with some more thyme, salt and pepper. Chill until needed or bake straight away.
Preheat the oven to 200°C (180°C fan oven) Gas Mark 6. Poke a steam hole in the centre of the pastry then bake the pie for 30 minutes, or until the pastry is puffed and golden.