Pull the currants gently off their stems. Rinse and set aside. Finely chop the zest (or zest with a microplane). Set aside.
Butter a 10-inch cake pan; line bottom with parchment or wax paper. Preheat oven to 350° F.
Using an electric mixer (paddle attachment if you have one), cream butter and sugar until light. Mix in the oil. Add eggs and mix until smooth. Scrape sides and bottom of the bowl.
With mixer on low speed, add the baking powder and 1 cup of flour. When well combined, add half the milk, another cup of flour, the rest of the milk, and the rest of the flour, mixing well after each addition. Stop to scrape the bowl as necessary.
Remove the bowl from the mixer and gently fold in the currants and orange zest. Pour the batter into the prepared pan and bake until golden brown and firm on top, about 50 minutes.
Cool on a rack to room temperature. Serve with lightly whipped unsweetened cream.