Fry the mince in a hot non-stick pan, stirring to break up any lumps, until nearly browned. When the fat runs add the chopped vegetables and cook for 5-8 minutes until beginning to soften and the meat is brown all over. Stir in the flour and cook for a minute or two.
Add the stock, tomato puree and Worcester sauce, stir well and bring to the boil, then reduce the heat , partially cover with a lid and simmer for about 40-50 minutes until the juices are thick, rich and bubbling and the meat and vegetables are tender. Cool the mixture a little then stir in the horseradish.
Spoon the mixture into a 2 litre gratin dish or 6 individual dishes, 350g capacity.
Cook the potatoes in boiling water until very tender, about 15-20 minutes. Put the milk, butter, salt and pepper into a small saucepan ready to heat up when you drain the potatoes.
Preheat the oven to 190 C/ 170 C fan/ gas mark 5. When the potatoes are ready, drain them well then give the pan a firm shake or two to smash them up and allow the steam to escape.
Mash well with a fork or masher till there are no lumps then beat in the warm buttery milk with a fork to keep the mash light and airy. Check the seasoning.
Spoon the mash evenly over the top of the meat and evenly spread to completely cover and seal in the meat, especially at the edges. Dot the top with a little extra butter if you wish and bake in the oven for 30-40 minutes for a large dish or 15-20 minutes for the individual servings until bubbling and golden.