Combine the yeast, sugar and 1tablespoon of the flour in a small bowl. Add the milk and mix until smooth. Leave in a warm, draught-free place for 10 minutes, or until bubbles appear on the surface. The mixture should be frothy and slightly increased in volume. If your yeast doesn’t foam, it is dead, so you will have to discard it and start again. Place the remaining flour in a large bowl and rub in 125g (4½oz) of the butter with your fingertips. Stir in the extra sugar, lemon zest and half the mixed spice. Make a well in the centre, add the yeast mixture and egg and mix. Gather together and turn out onto a lightly floured surface.
Knead for 2 minutes, or until smooth, then shape into a ball. Place in a lightly oiled bowl. Cover with plastic wrap or a damp tea towel and leave in a draught-free place for 1 hour, or until well risen. Punch down and knead for 2 minutes, or until smooth.
Preheat the oven to 210°C (415°F/Gas 6–7). Lightly grease a baking tray. Beat the remaining butter with the brown sugar in a small bowl using electric beaters until light and creamy. Roll the dough out to a 25 × 40cm (10 × 16inch) rectangle. Spread the butter mixture all over the dough to within 2cm (¾inch) of the edge of one of the longer sides. Spread with the combined fruit and remaining spice. Roll the dough from the long side, firmly and evenly, to enclose the fruit. Use a sharp knife to cut the roll into eight slices about 5cm (2inch) wide. Arrange the slices, close together and with the seams inwards, on the tray. Flatten slightly.
Cover and set aside in a draught-free place for 30 minutes, or until well risen. Transfer to the oven and bake for 20 minutes, or until brown and cooked. When almost ready, stir the extra milk and sugar for glazing in a small saucepan over low heat until the sugar dissolves and the mixture is almost boiling. Brush over the hot buns. Cool.
To make the icing, mix the icing sugar and milk, stir until smooth, then drizzle over the buns.