Butter an ovenproof dish and heat the oven to 180C/160C fan/ gas 4. Carefully weigh out the butter and sugar into a bowl.
Finely grate the zest from the lemons. For best results, grate, then turn the lemon a little and grate again, so you just take off the yellow skin rather than the pith below. Halve and squeeze the juice from the lemons - you need 100ml, so make up with a splash of water or more juice.
Separate the eggs (put the whites in a large, clean bowl), being careful not to get any yolk in with them. Whizz the butter, sugar and zest in a food processor until creamy. Add the juice, whizz again; then, with the motor still running, tip in the yolks, flour and milk to form a smooth batter.
Whisk the egg whites, preferably with an electric hand whisk, until firm but not stiff. Pour in the lemon batter, then gently fold the 2 mixtures together with a large metal spoon, being light-handed so that you don’t knock out all the air from the whites. Don’t worry if it looks a bit lumpy.
Pour the mixture into the buttered dish, then put it in a roasting tin. Pour in a kettle of hot water into the tin so it is half-filled (this is called a bain marie). Ask an adult to help you with this bit. Bake for 35 mins until the top is set and there is a saucy lemon curd below. Use oven gloves to remove it from the oven.
While the pudding is baking, pull or cut the hulls (the green tops) from the strawberries. Halve or slice them if large. Put in a bowl with the blueberries, then spoon over the cordial or sugar and mix together. Remove the pudding from the tin, dust with icing sugar through a sieve and serve warm or cold, with the berries.