Campaigning group Farmers For Action (FFA) called the strike, which began Wednesday, asking all dairy farmers to dispose of their milk or simply hand it out rather than sending it to dairies.
FFA chairman David Handley said the move was a protest against low farmgate milk prices in Britain.
Processors currently pay producers an average of 18p per litre, down from 25p back in 1996 and easily the lowest price in the old 15-member European Union, according to the Milk Development Council. The average cost of producing milk is about 20p per litre in the UK.
But, the FFA's three-day strike has failed to garner enough support among dairy producers, and others were sceptical about its claim that 4,000 farmers would take part.
"Our information is that it doesn't have a wide range of support. We have told our members not to get involved," said a spokesperson for Britain's National Farmers' Union (NFU), the country's biggest dairy farmers union.
"While we understand the reservations that many farmers have concerning the price pressure on their milk, we don't believe that strike action will achieve what farmers actually want. This is not going to be a silver bullet in the on-going process of getting a more sustainable milk price."
The NFU, despite criticising farmgate price cuts by dairy processors earlier this year, said it had informed processors and retailers of its opposition to the FFA protest. "We have to work with these guys because they buy our products."
The NFU said in its Dairy Vision report last month that producers needed to work constructively with processors and retailers, particularly focusing on a better contracting system to boost earnings across the sector.
The union said that, while processors must invest more to develop added value products that can compete with foreign firms, producers themselves must "adopt a more business-like approach". It added that consolidation in the industry would be painful but necessary.
The sector has certainly been under pressure in the last couple of years. A recent report commissioned by agriculture ministry DEFRA warned that the country was "facing a worst case scenario" of milk production falling to more than one billion tonnes below quota by 2007/08.
More worryingly, a major reason for this was that greater numbers of larger, more efficient dairy producers had left the industry than was originally forecast.
Retailers, meanwhile, have increased profits on liquid milk by a quarter in the last 10 years and more rapidly since 2003. This has put pressure on processors such as Arla and Dairy Crest, who have in turn reduced farmgate prices to protect margins.