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Heat the oven to 350 degrees F and grease a 10" or 11" cake tin.
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Finely grate the zest from two of the oranges into a large bowl.
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Cut the peel and pith from all of the oranges with a serrated knife, and slice quite thickly.
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Drizzle the golden syrup on the bottom of the cake tin.
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Arrange the best orange slices on top of the syrup and finely chop any that don't fit.
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Put all of the remaining ingredients into the bowl with the orange zest and chopped orange.
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Beat with an electric hand mixer until smooth.
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Spoon on top of the oranges, spread lightly and make a deep hollow in the centre of the mix with the back of a spoon - this will ensure that the cake rises evenly.
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Bake for 45 to 50 minutes until firm when pressed.
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Allow to settle for 5 minutes before turning out.
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Drizzle with additional golden syrup if you like and serve with custard or ice cream.