Set the oven to 180C/350F/Gas 4 (160C fan).
Rub the butter into the flour until it resembles fine breadcrumbs (this can be done in a food processor). Stir in the sugar and cinnamon.
Peel the apples, core and dice two and a half apples and stir into the cake mixture with the eggs. Beat until combined.
Divide the cake mixture evenly between the cake tins. Thinly slice the remaining half of apple and arrange in a row along the middle on top of each cake. Sprinkle with demerara sugar and bake for 35-45 minutes, or until golden-brown, risen, firm to the touch in the centre and just shrinking from the sides of the tin.
Brush the top of the cakes with the apricot jam. Allow to cool in the tins for 10 minutes, then turn out and leave to cool on a wire rack.