Story about a mother and her children at an apocalyptic event

This might be a long shot,but I am trying to remember a short story set in Britain after some sort of apocalyptic event with a mother and her children. The mother had just given birth and the baby was dying or too little, and the mother was trying to overdose her other children by putting medicine in icing on biscuits. That’s all I remember unfortunately, hence the long shot. I can’t even remember if I have read it or if it was a radio play: if so it would have been on radio 4.
Anyway, just throwing it out there.

In Nevil Shute’s On The Beach, which takes place after a global nuclear holocaust, parents poison their baby by putting a drug in her bottle.

StG