Cream the butter and 250g of the sugar together until well combined. Add the oil and finely grated lemon zest from all three lemons and beat until light and fluffy.
Beat in the eggs, one at a time. If the mixture starts to curdle, add a little of the flour.
Sift in the the flour, baking powder and bicarbonate of soda and discard any particularly large peices of bran. Fold in, together with the ground oats, until just combined. Carefully stir in 75ml hot water followed by the poppy seeds.
Scrape into a 22cm (9") square silicone cake mould or lined tin and bake for 40-45 minutes, or until an inserted skewer comes out clean.
Meanwhile, heat the remaining 150g sugar with the juice from two of the lemons until just dissolved. Make a few holes in the hot cake with a skewer then pour the syrup over the top.
Leave to cool completely before cutting into 16 squares.
Notes
Adapted from a Dan Lepard recipe in Short and Sweet.Please note: calories and other nutritional information are per serving. They're approximate and will depend on serving size and exact ingredients used.