Put the milk and butter in a small pan over a low heat, until the butter is melted and the mixture is lukewarm, but not hot.
Put the flours, sugar and salt into a large mixing bowl. Make a well in the centre and add the yeast. Pour in the butter and milk mixture and the beaten egg, plus the mixed spice and lemon zest. Stir until combined into a soft dough.
Knead the dough for 5 minutes using a stand mixer fitted with a dough hook on a low speed, or for about 10 minutes by hand, until the dough is soft and elastic. Put the dough in a lightly oiled bowl and cover with cling film or a damp tea towel. Leave to rise in a warm place for an hour or so, until roughly doubled in size.
Give the dough a quick knead with your hands, then roll out onto a lightly floured surface into a large rectangle, about 30 × 20cm and about 4mm thick. Spread the softened butter evenly over the dough. Scatter over the brown sugar and the spices, then the fruit. From the longest edge, roll the dough as tightly as possible to create a log shape, as if making a Swiss roll; use a dab of water on the long edge of the dough to seal the roll if needed. Using a sharp knife, cut the roll into 9 slices.
Arrange the rolls, spiral side facing upwards, in a baking tin or tray that measures about 35 x 25cm. Try and leave just a small gap between each one – the rolls traditionally squish together during baking so you can ‘tear and share’. Cover the tray and leave to rise for 30 minutes.
Preheat the oven to 190°C/Fan 170°C/Gas Mark 5. Bake the rolls for 20–30 minutes, until risen and golden (if the fruit looks like it is burning at any point, cover the rolls with kitchen foil).
Leave the buns to cool slightly while you make the icing. Simply combine the icing sugar with the lemon juice or water – it should be very thick. Move the buns onto a cooling rack and drizzle with the icing. Enjoy while still warm.