Survival of the Post nuclear food serfdom

How did 4 million survive the nuclear winter? The nuclear winter likely leeched lots of nutrients from the soil,along with environmental damages from nuclear war and chemical spills as well as trees being cut down for fires. The food stocks of the British Government was going to run out eventually, and food scavanged from the ruins is going to go bad eventually. During the first harvest the British used all their agrochemicals, the post nuclear winter crops are defenseless agianst insects and viruses. To the credit of the Yorkshire government much of the crop of the first harvest was already sown before the nuclear attack and seed reserves are avaliable for subsequent harvests and mechanization was introduced using steam power. The post british governments also cannot survive with such meager crops and can’t build more steam engines if it can’t survive. The death of 40 million humans, dogs and other animals also fertilized the soil but eventually this source of soil nutrients is going to run out. So how did 4-11 british survive if the environment is recovering so slowly