Paul Tompkins, who farms at Melbourne in the Vale of York, made the plea after farmers elsewhere in the country filmed themselves 'dumping' fresh milk due to falling demand.
Mr Tompkins has a herd of 250 dairy cows and has been badly impacted by the shutdown of the restaurant sector. He is currently losing £165 a day compared to his income before the coronavirus crisis and is unable to access government support schemes.
Although he supplies small supermarkets and garages, other orders came from leisure centres and hotels which have now closed.
"Three weeks ago I had a viable business," he said.
"Through no fault of my own, the government has turned off a large proportion of my customers. Unlike, say, a hotel, we can't furlough staff, because the cows still need milking, and we can't apply for cash grants.
"It's a worrying time. We need to think about milk supply when all this is over. If I turn off my supply, I can't just turn it back on again."
Mr Tompkins said he was not yet having to pour away unused milk, but knew of farmers in the south of England who were.
He said he hoped that the crisis would make the country think hard about the importance of its domestic food supply industry ahead of anything similar happening in the future.
Environment secretary George Eustace is now meeting with the NFU for urgent crisis talks after videos emerged of milk being poured away on farms. At least 2,000 dairy farmers are thought to be affected.
The union has suggested that contracts to supply milk to the NHS, military bases and prisons could be awarded instead to provide an income stream.
A Defra spokesman said: "We have taken a number of measures to support our food and farming sectors to manage the impact of coronavirus on the dairy supply chain.
"We are also working very closely with farmer and processor representatives to understand the specific challenges that the dairy sector is facing.
"Frequent discussions with the dairy supply chain will continue through this crucial period to understand what further support the sector needs.
"We have been working closely with the NFU and other stakeholders, and the Secretary of State will also be speaking directly to the NFU President to discuss this matter further."