Preheat the oven to 350°F, 160°C-170°C, or gas mark 3–4.
In a large pot over medium heat, boil potatoes until tender, drain well and mash until creamy.
In a mixing bowl, add the mashed potatoes, butter, sugar, and oil and blend well with a whisk or hand mixer.
In a separate bowl, whisk eggs.
In a small bowl or mug, mix the custard powder with 1 cup of milk, and add to the whisked eggs.
Add the remaining 3 cups of milk to the egg mixture and stir well.
Combine the egg mixture with the mashed potato mixture, and stir well.
Pour half of the batter into a well greased 11" x 15" (30 x 40cm, or similar) oven roasting pan.
Put the half-filled dish into the oven, in the center of the middle rack, and add the remaining batter.
Bake at 350°F, 160°C-170°C, or gas mark 3–4, for 1 hour.
Cover the pudding with foil, and bake for a further 15 minutes.
Remove from the oven and let pudding cool and set at room temperature for a minimum of 6 hours, or overnight.
Serve warm or cold, with mixed berry compote, or stewed dried fruit.