Preheat oven to 180C/350F. Grease two 24cm x 32cm (9 1/2-inch x 13-inch) swiss roll pans; line bases and long sides with baking paper, extending paper 5cm (2 inches) over sides.
For the ginger cake, sift flours, bi-carb soda and spices into a large bowl; stir in brown sugar. Combine butter and syrup in a small saucepan; stir over low heat until smooth. Stir butter mixture into flour mixture along with egg and milk. Divide mixture between pans; bake for about 10 minutes. Cool in the pans.
Meanwhile, make lime filling. Sprinkle gelatine over juice in a small heatproof jug. Stand jug in a small saucepan of simmering water and stir until gelatine dissolves. Cool for 5 minutes. Beat cream cheese, sugar and rind in a medium bowl with an electric mixer until smooth, then beat in cream. Stir in gelatine mixture.
Pour filling over one of the ginger cakes in the pan; top with the remaining ginger cake. Refrigerate for 3 hours overnight until firm before cutting into 32 pieces.