Last week the company staged another protest in Cardiff, Wales, claiming that, "a number of UK supermarkets and dairy companies are still allowing their suppliers to feed their cattle GM ingredients".
Marks and Spencer remains the only major UK retailer to stock its entire milk range produced from animals fed on organic feed, although the UK's third largest supermarket Sainsbury's has rolled out similar milk trials across 190 of its stores, displayed alongside its existing range of organic, gold top and standard milks.
"All our milk is GM-free, although we do stock some milk which has been made from cattle reared on GM ingredients," Sainsbury's commented.
"We give our customers a choice. Milk which is sourced from non-organic ingredients is clearly labelled to avoid any confusion."
The UK's food industry regulator, the Food Standards Agency (FSA), together with several science and industry bodies, last year produced extensive research showing that neither GM DNA or protein was found in milk samples orginating from cattle reared on GM feed.
The British Retail Consortium, the trade association for UK retailers, lambasted Greenpeace for "creating unnecessary food fear through misleading claims that are without scientific foundation".
"Retailers in Wales and the rest of the UK provide total choice for their customers when it comes to milk. Whatever a customer needs, they can find it on the shelves and make an informed decision on what they buy," it added.
Greenpeace estimates that British dairy producers could change their feed ingredient arrangements from GM to non-GM for less than 1p per litre, although it argues that supermarkets - not farmers - would be best placed to accommodate this cost due to the sizable margins they reap.
But it appears that this suggestion remains impractical to implement and somewhat contentious.
"We are not able to make decisions for what is essentially a farmer's individual choice," Sinead Noble, a spokesperson for Dairy Crest told DairyReporter.com.
"Even if all our supplier farmers wanted to use non-GM feed then it would be impossible, as there is currently a deficit in the UK. In fact it would take around seven years to produce the necessary organic feed volumes required by the UK dairy industry," she added.
According to Greenpeace, the UK's three largest milk producers Arla Foods, Robert Wiseman and Dairy Crest all use milk that has been sourced from some GM-fed cattle.
The majority of the UK's cattle feed is imported from the US and South America and the US Department of Agriculture claims that approximately 30 per cent of US-produced maize is GM, while only 15 per cent of US crop plantings in 2004 were produced using non-GM farming practices.
In 2003, the UK imported approximately 21.3 million tons of soya beans and soya bean meal from the USA, Canada, Brazil and Argentina.
Furthermore, the UK imported around 0.75 million tons of maize gluten feed from the US, in addition to smaller quantities of rapeseed and cotton meal from other parts of the world.