Ministers are drawing up contingency plans to keep products on shop shelves if farmers step up protests over inheritance tax but have also promised that no-one will have to go without food.

Farming leaders insisted that they did not condone strikes that led to food shortages, but warned that feeling was running high over what they described as a “betrayal” of the countryside.

Daniel Zeichner, the farming minister, urged farmers to calm down, saying that “the vast majority will be fine” and criticising “extraordinary” claims about the numbers potentially affected.

Up to 20,000 farmers are expected to gather in Westminster on Tuesday to protest against the government’s decision to impose inheritance tax on farms worth over £1 million. Farmers have claimed that the policy will mean the end of family farms but ministers insist that only the biggest estates will be affected.