I've wanted to try a recipe for a Madeira cake. Why is it called this? Is it used a lot for fondant cakes and is it a firm texture?

It is a moist, dense lemony spongecake yes....quite like North America pound cake.

It's called a "Madeira cake" because it was popular to moisten it with Madeira wine before serving it.....or even to serve it with a glass of the wine.

Madeira Cake
1 1/2 sticks [6oz] butter, at room temperature
6 oz sugar [little less than 1 cup]
3 large eggs
2 1/4 cups [9oz] self-raising flour OR
2 1/4 cups [9oz] all purpose flour PLUS
3 teaspoons baking powder PLUS
1/2 teaspoon salt
3 tbsp milk [can use lemon juice]
1 lemon, zest only
Method: Pre-heat the oven to 350F. Grease an 7in round cake tin or 6in square cake tin, line the base with bakingpaper and grease the paper.
Cream the butter and sugar in a bowl until pale and fluffy. Beat in the eggs, one at a time, beating the mixture well between each one and adding a tablespoon of the flour with the last egg to prevent the mixture curdling.
Sift the flour and gently fold in, with enough milk to give a mixture that falls slowly from the spoon. Fold in the lemon zest. Spoon the mixture into the prepared tin and lightly level the top. Bake on the middle shelf of the oven for 30 minutes.