Heat the oven to 180 C / 350 F (160 C fan / 320 F). Grease a 20 cm / 8-inch square baking tin and line it with parchment, leaving an overhang on two sides.
In a mixing bowl, whisk together the flour, baking powder, ground ginger, cinnamon, and salt.
Rub the cold, cubed butter into the flour mixture with your fingertips until it looks like coarse breadcrumbs.
Stir in the demerara sugar and light brown sugar until evenly distributed through the crumbs.
Warm the golden syrup for about 10 seconds so it loosens, then drizzle it in. Mix with a fork, then bring the mixture together with your hands into a crumbly dough that just holds when pressed, not smooth like cookie dough.
Tip the mixture into the prepared tin. Press it firmly and evenly with the back of a spoon or the bottom of a glass, packing it into the corners.
Bake for 22 to 25 minutes, until the edges are deep golden and the center still looks pale and slightly soft. It firms up as it cools, so pulling it out a touch early beats overbaking it hard.
Remove from the oven and score into 16 squares with a sharp knife while it's still in the tin. Do not cut all the way through yet.
Cool completely in the tin, at least 1 hour, before cutting through the scored lines and lifting the squares out.