Asda has played down claims it has threatened UK farming group Farmers for Action with legal action after recent protests at the retailer's sites.

Farmers for Action claimed earlier this week that Asda had warned "various co-ordinators" within the group of possible legal action.

Asda is among a number of UK retailers and dairy processors that have been targeted by protesting farmers angry at planned cuts to the price of milk.

On its Facebook page, Farmers for Action said: "Through their lawyers, Eversheds, Asda are threatening legal action against various FFA co-ordinators. They have tried this on once before, in 2010, went to court and it was thrown out. Whilst this will prevent the named people being seen organising various actions, we obviously have plenty of people in the background who will move forward, so the action will still continue as usual against Asda."

A spokesperson for Asda said the retailer had written to Farmers for Action to remind them of a deal between the two sides last year.

"As for the 'threat of legal action' – have you seen the letter?" the spokesperson said. "We simply sent a letter to the seven main organisers of the FFA to remind them of an assurance they gave us in 2011 that before taking any action against our business, they would engage in discussions with us first and exhaust all other forms of debate. As we'd had no contact from them prior to their action at our Dartford Depot last week, we simply wrote to remind them of that agreement."

Asda has come under fire for the price it pays farmers for milk. After initial protests at its stores, Asda last week increased the premium it pays by 1p to three pence per litre. Farmers for Action chairman David Handley called the increase "an insult".

The retailer again lifted its premium this week to farmers in its DairyLink pool. Farmers in the scheme will be paid 29.5ppl from 1 August, which Asda said was 5p above the Arla Foods base price. Arla is one of the processors planning to cut prices next week.

Farmers have said the cost of milk production is 30ppl. Costs could increase this winter with recent wet weather affecting fodder crops. The cost could lead farmers to reduce the amount of milk they produce, putting pressure on the UK milk supply.

The Asda spokesperson added: "Our discussions about the premium we pay have been with our farmers based on their concerns. Also, remember the farmgate price paid is decided between the producers and the processors – not the supermarkets."