1.Preheat oven to moderate. Grease 25cm x 30cm swiss roll pan.
2.In a small saucepan, bring dates, water and honey to a boil. Simmer, uncovered, 2 minutes or until slightly thickened; cool.
3.In a small bowl, beat butter and sugar with electric mixer until combined. Stir in sifted flours and nutmeg, date mixture, bran and banana. Spread mixture evenly over base of prepared pan.
4.Bake in moderate oven about 30 minutes or until firm; stand 20 minutes. Spread with lemon icing; sprinkle with a little extra nutmeg.
5.Meanwhile, sift icing sugar into small heatproof bowl; stir in butter and juice and enough water to give a stiff paste. Stir over pan of simmering water until spreadable.