Hmmm, I would take the the onions, mushrooms and leeks and saute them in a wee bit of butter, adding salt, pepper, 3 cloves of garlic, (hey, I like my garlic) , set aside.
Take two pieces of bacon and cook till crisp in an unoiled frying pan, keep the oil ( the bacon fat adds alot of flavor to the minced beef) and throw out ( or eat) the bacon, then add your minced beef. Fry until brown, adding salt and pepper, add your mushroom, onion and leek saute in and 1/2 a cup of red wine, cook until liquid reduces by half. Add just a touch of double cream to emulsify.
Take your potatoes, and turnip and slice thinly, so they almost look like potato chips or crisps as you would call them, and julliane the carrots (that means, cut them to look like matchsticks, very thin and small) .
Preheat oven to 325 F, hmm not sure how hot that would be on a brit range. Maybe someone could help out with that.
Layer one layer of potato, turnip and carrots, then the minced mix in the bottom of a cassorole dish and repeat until you are left with several layers. Cover the top with your choice of cheese, if you wish and then cover with aluminum foil. Bake for 45 minutes and then remove the foil, turn on the broiler (top element only in stove) just until the top of the dish begins to bubble and turn golden brown.
Ta da, done. It might take a little longer prep time, but the result is yummy and its great for leftovers!! Just cut into squares and package for lunch the next day.