I made the Lemon Meringue Cake once without problems. However, this time the cake was raw and the meringue dark after 20 mins. I tried to cover the cakes with greaseproof paper but they couldn't be saved so I binned them. I tried again but the same result and the same fate for the cake. The meringue seemed to form an insulating blanket through which the cake couldn't cook.
Nigella's Lemon Meringue Cake (from FEAST) is a thin sponge cake that is topped with meringue before baking. The cake batter layer is very thin and so should cook within the time it takes for the meringue to brown on top. From the description it sounds as if the oven could have been a little too hot. The oven temperatures in the recipes are for conventional ovens so if you have a fan or convection oven then you would need to adjust the temperature following the instructions in your oven handbook.
For a conventional oven make sure that the cakes are being baked no higher than the middle shelf, as if they are too high in the oven then the top of the meringue could brown more quickly. If you have a conventional or a convection oven that has a heating element at the top of the oven then use a lower shelf to keep the top of the meringue away from the radiant heat source.