Preheat oven to 175 degrees C. Grease and flour a 22x13cm loaf tin. In a saucepan over medium heat, bring dates and water to a boil. Add the butter and sugar and stir until melted. Remove from heat and stir in bicarbonate of soda. Let cool for 10 minutes.
Place date mixture into a large bowl. Blend in flour, egg and vanilla. Stir in chopped walnuts and pour batter into loaf tin.
Bake for 50 to 60 minutes, or until a toothpick inserted into the centre of the cake comes out clean. Let cool in pan for 10 minutes, then turn out on to a wire rack and cool completely.
To make brown sugar sauce: In a saucepan over medium heat, combine the butter, cream and sugar. Heat, stirring constantly, until mixture boils and sugar is dissolved.