They also held marches to campaign against processors cutting up to 2p a litre off prices.

Their cause has been backed by celebrity chefs Jamie Oliver and Hugh Fearnley-Whittingstall who urged the public to boycott some supermarkets.

But the British Retail Consortium said supermarkets paid well and it was other purchasers who should be scrutinised.

Farmers targeted at least three milk plants.

The Robert Wiseman Dairy processing plant off junction 24 of the M5 near Bridgwater in Somerset was blockaded by between 600 and 700 farmers with their tractors on Thursday night.

Farmers also staged a protest outside the Arla plant in Leeds, while 400 farmers also gathered outside the Arla plant in Ashby-de-la-Zouch, in Leicestershire.

Organisers there delivered a letter to the site manager asking for the reinstatement of previous prices and said they would not move until they got a response.

Farmer James Small, from Somerset, said at the Bridgwater protest: "I think it's a fantastic showing of unity here.

"There are an awful lot of young people who obviously want to have a future in dairy, and farming in general, and they're voicing their concerns about whether there will be a future given the current crisis.

"The sense of frustration and anger is palpable amongst the people here, they all feel a huge injustice about it all.

Farmers for Action (FFA) planned marches in Staffordshire, Leicestershire and Yorkshire.

Andrew Hemming, the vice chairman of the pressure group, said: "We want all dairy farmers to receive a milk price which covers their production and allows them to make a small profit for them to be able to supply the country not only for the next six months but the next 20 years."

How much is a pint of milk?

He said the group was concerned about continuing the supply of milk, adding that hundreds of dairy farmers could be forced out of business by price cuts which would lead to milk being imported in large quantities.

In a letter to the Times Mr Oliver - who used to promote Sainsbury's - and Mr Fearnley-Whittingstall wrote: "It's time supermarkets stopped using milk as a loss leader. And if they won't take that initiative, then perhaps consumers will consider moving their custom from those who offer milk at crazy knockdown prices to those who will commit to giving dairy farmers a fairer deal."

Later, Mr Fearnley-Whittingstall told the BBC: "Supermarkets need sensible and sustainable contracts.

"I'm personally in favour of independent retailers, local shops, including farm shops and the like.

"Many of them source directly from local dairies, which means there's a better chance of a fair price getting back to local farmers."

Asda, Morrisons and the Co-operative have previously pointed out they pay a premium above the market price charged by suppliers - but Mr Fearnley-Whittingstall said the dairy farmers were targeting the three chains as they had the "most punitive and least sustainable" contracts.

"All of those supermarkets make a lot of PR [public relations] noise about how supportive they are of dairy farmers, so there's a hypocrisy factor here that the NFU want to emphasise," he added.

Hugh Fearnley-Whittingstall's response

Supermarket contracts with dairy farmers vary hugely.

Farmers... are in no position to take industrial action or even leave contracts for fear of going bust immediately.

Other businesses who buy large amounts of milk are also guilty of enforcing these harsh contracts - and we may expect to see more names revealed by dairy farmers and the NFU that represents them in the coming days.

But the supermarkets are the biggest players by far, and if they were to lead with fairer contracts, there's a strong feeling that others in the sector will follow.

But Sarah Cordey of the British Retail Consortium (BRC) said supermarkets were the "wrong targets" in the campaign.

"Eleven of the 12 best paying customers for milk are paid by supermarkets and are under a lot of public scrutiny," she said.

"We are surprised that we don't see farmers or TV chefs asking important questions of manufacturers or the public sector about the price they pay for milk."

The BRC estimates that about half of the milk British farmers produce ends up as liquid milk in bottles and cartons and only part of that is sold in supermarkets.

The remainder is thought to be sold by convenience shops, door-to-door or used in catering, schools and prisons.

It said dairy processors, manufacturers and the public sector should be held accountable in the same way as retailers.

Farming Minister Jim Paice said the price cuts were a "severe blow" for dairy farmers.

"Government cannot and should not set prices but I will do everything in my power to get all levels of the supply chain to make the real changes needed to guarantee the industry's long-term future," he said.

"Farmers and processors need to work together through an industry code of practice on contracts, and retailers have to help shift the focus away from short-term practices which are completely unsustainable."

Meurig Raymond, of the National Farmers' Union (NFU), has said dairy farmers from across the UK had been "pushed to the brink" by cuts to the price of milk.

In a statement, Arla Foods said the business was owned by farmers and was run in their interests.

"We are deeply concerned about the pressures the recent price cuts are having on our farmers. It's a tough time and we are not happy about the situation," it said.

"Reducing the milk price is always the last resort. We literally have exhausted all other options. We are working very hard to secure better returns for our supplying farmers."

In the dairy industry, the processors set the price they pay farmers for their milk.

Four leading dairy processors recently announced the latest cuts - applied from 1 August.

Robert Wiseman Dairies and First Milk have both cut the price by 1.7 pence per litre (ppl), Arla Foods UK by 2ppl and Dairy Crest by 1.65ppl.

Price cut impact

The processors blame falling commodity prices.

They say they have had no choice but to pay less for the product, because the price of cream on the commodities market has fallen sharply in the past 12 to 18 months.

Milk processing in effect involves skimming off cream to make milk more palatable for consumers. So the processors say if they are making less money selling cream, they have less money to pay for the milk.

The cuts would be felt by 27% of producers, and impact on 25% of the milk market volume, farmers' union NFU said.

It said an average farmer, with about 150 to 200 cows, would lose about £37,000 in revenue from the combined effect of cuts in May/June and August.

Those cuts would not affect farmers supplying Tesco, Sainsbury's, Marks & Spencer or Waitrose as they are paid directly by the supermarkets.