The turquoise placards held aloft outside the factory in Wigan summed up the feelings of the 1,200 or so striking workers: "Heinz Beanz is being really meanz."

For the third week in succession, workers at the factory, which produces 2m cans of beans and soup every day, staged a 24-hour walkout, with a fourth strike planned next week. The plant, visible from the nearby M6 – it has a huge 57 illuminated on its side, a nod to its "57 varieties" slogan – from the American company's early days is one of the company's oldest in Britain, and has been producing beans for almost 51 years.

Heinz has clashed with its workforce after it rejected a two-year pay offer which the union says is worth 3.3% this year and 3% for 2011. Unite said millions of cans were lost from production during last week's strike, although the company was keen to maintain there would be no need to hoard beans, soup or baby food for fear of shortages.

"The mood among the workers has become very strong and it is very anti-company," said Heinz worker Mick Quinn outside the factory today. "The members would never decry the brand itself; the argument is between the members and the management for a better and a fairer deal." He said there was no sign of the situation being resolved. "The offer has not changed enough to warrant another mass meeting."

A day-shift engineer said there were 250 managers on site taking bonuses who "don't know what they are doing". He said: "We are the people running the machines and we are getting nothing. I think Wiganners believe in principles and we are not being treated fairly."

Ian Wright, Unite's convener at the plant, said: "The workers are a huge part of what makes the company a success but they are not being treated well and not rewarded. The shareholders and management are rewarded but not the workers."

He said they felt passionately about what they do and did not want to harm the brand. "But unfortunately the only silver bullet the working man has is to strike."

The two sides held talks before Christmas with the aim of resolving the dispute. Taking issue with the union, a Heinz spokesman said the pay deal was worth the equivalent of 4% this year and 3% in 2011, describing the offer as "one of the best pay offers in the industry". He said: "The pay talks resulted in a revised offer being put to the Unite union negotiating team including the reinstatement of a performance-related bonus. Unite rejected the offer and are not willing to put it forward for consideration by Heinz workers. We are extremely disappointed with this outcome."

Heinz claims workers at the plant are paid 30% more than the average for people doing similar jobs in the industry, adding that a third of its staff had worked at the factory for more than 21 years which, the company said, was a reflection of its pay and benefits.

Although it is an American company, many Britons regard Heinz with affection. It has been selling cans of beans since 1895 and introduced them to Britain on the shelves of Fortnum & Mason in 1901. It now sells 442m tins a year in the UK and its 1960s advertising slogan, Beanz Meanz Heinz, was voted the best slogan of all time by a panel from the British advertising industry.

Unite leader Len McCluskey, who visited the plant today, accused the company of behaving in an unpalatable manner. Unite has accused the company of hypocrisy, with 15% bonuses for well-paid managers but a real-term pay cut for ordinary workers.

McCluskey said people in the UK are fond of Heinz products, as sales show, but they also admire fairness. "If they understood how Heinz is squeezing workers' wages to instead turbo-charge profit margins and put money in the pockets of managers, then that affection would certainly be tarnished," he said.

The pay offer, the union claims, is far adrift from the current rate of inflation. "When [workers] rightly decide to stand up and win better for themselves, their good conduct and loyalty over the years is rubbished by Heinz," McCluskey said. "By any standards, this is breathtakingly unfair. He described his extreme disappointment that management used last week's talks to worsen the offer, adding: "There's a new year around the corner, we urge Heinz to adopt a new attitude with it."

Unite national officer Jennie Formby said: "The company is shamefully trying to smear this workforce as grasping for more cash even though, year on year, they have worked extremely hard to deliver whacking great profits for Heinz.

"With Heinz's profit margins extremely healthy at 37%, the workers rightly feel that the company is vastly wealthy and can easily afford to help them meet the spiralling costs of living."