I have just had a PM from another mumsnetter who used this recipe when I posted it last year. She said that it was delicious. 30cm x 40cm is basically 12 inches x 16 inches so you could increase the mix by 1/3rd. It shouldn't make any real difference to the cooking time as the middle of the cake is still 6 inches from the side.
Madeira Cake - 12? Square (Cooking time 65 mins)
Ingredients:
825 gm Butter
825 gm Self Raising Flour
825 gm Caster Sugar
12 Large Eggs
Method:
Pre-heat the oven to 180 deg. (Gas Mark 4)
Grease and line the pan (Triple lining is suggested to prevent scorching).
Take a LARGE mixing bowl, cream the butter and sugar. Then add the eggs, one at a time to prevent curdling (you may need to add a little flour from time to time). Once the eggs are mixed in, fold in the balance of the flour.
Cook for 30 minutes at 180 deg. then cover with baking parchment for another 20 minutes at the same temperature. For the final 15 minutes, keep covered but reduce the temperature to 170 deg. (Gas 3).
This should produce a cake that has a close, even texture, is completely cooked and moist.