Weigh the flour into a large bowl. Add the easy bake yeast, sugar and salt and mix.
Measure the milk and water and pour into a saucepan. Add the butter. Heat gently until the butter has just melted and the mixture is hand not and then stir.
Add the hand hot milk/water/butter mixture to the bowl of dry ingredients whilst it is still hand hot so that it is the right temperature for the yeast.
Add the egg and stir with a fork. Mix with an electric mixer with dough hooks attached for a few minutes.
Form the dough into a ball adding a little extra flour if the dough is sticky. Cover the bowl with a large plate and leave in a warm place to prove for around an hour.
To assemble
Place the dough on a floured pastry board and carefully stretch to form a rectangle about 30cm by 40cm (12" by 16").
Thinly spread the mincemeat over the dough leaving a small gap around the edge.
Roll the dough to form a roll 30cm (12") long, ie, the shorter edge of the rectangle will be the length of the roll.
Use a sharp knife to cut the roll into 12 equal slices. If the dough is squashed where it is cut by the knife simply reform using your fingers.
To bake
Lightly oil and line the baking tin. Arrange the pinwheels in the tin leaving a small gap between each one to allow room for expansion.
Leave in a warm place to prove for an hour or so before baking.
Bake at 170°C, 325°F, gas mark 3 until they look ready and are slightly golden on top (around 20 minutes or so but check after 10 minutes and check again regularly to avoid overcooking). Turn the tin around part way through the cooking time.
To glaze
Prepare the glaze while the buns are baking. Place the sugar and water in a saucepan and heat gently until the sugar has dissolved.
Lightly brush the Chelsea buns with the glaze as soon as they are baked and whilst still warm.