Human rights lawyers are preparing to bring a landmark case against British American Tobacco on behalf of hundreds of children and their families forced by poverty wages to work in conditions of gruelling hard labour in the fields of Malawi.

Leigh Day’s lawyers are seeking compensation for more than 350 child labourers and their parents in the high court in London, arguing that the British company is guilty of “unjust enrichment”. Leigh Day says it anticipates the number of child labourer claimants to rise as high as 15,000. While BAT claims it has told farmers not to use their children as unpaid labour, the lawyers say the families cannot afford to work their fields otherwise, because they receive so little money for their crop.

The case, potentially one of the biggest that human rights lawyers have ever brought, could transform the lives of children in poor countries who are forced to work to survive not only in tobacco but also in other industries such as the garment trade.

It follows exposure of the scale and brutal reality of child labour in the tobacco fields by the Guardian last year, which Martyn Day, a founding partner and head of the firm, said had provoked them to act. “If it hadn’t been for the Guardian, this case would not be happening,” he said.

Day added: “It is totally depressing that one of the largest companies in the world, and certainly one of the largest British companies, is involved in an area where the employment of children is such a fundamental part of what happens. It has been going on for decades, and as a result of all of that the farmers of Malawi are caught in a groundhog day, where one generation after another is having to farm tobacco and is caught in a poverty trap.”

Many of the families are from Phalombe, one of the poorest regions in the south of the country. They are recruited to tobacco farms in the north with the promise of food, accommodation and a lump sum in cash for their crop. Their accommodation is a straw hut they must build themselves; the food is a monthly sack of maize, which is insufficient to feed the family and which is stopped before their tenancy ends. The lump sum they are paid at the end of the season dwindles often to less than half what is offered after deductions for tools and loans that the families have to take out to pay for essentials.

According to the letter of claim, last season most of the claimants earned no more than £100 to £200 for 10 months’ work for a family of five. Photograph: David Levene/The Guardian

According to the letter of claim, seen by the Guardian, last season most claimants earned no more than £100 to £200 for 10 months’ work for a family of five. Their lawyers say the work amounts to forced or bonded labour because they are misled when recruited, are afraid to leave and quickly get into debt.

Children as young as three are involved in tobacco farming, the letter of claim says, often during harvest when the work can be especially hazardous. Children are particularly vulnerable to the effects of toxic pesticides, fertiliser and green tobacco sickness, from nicotine absorption while handling the leaves. Symptoms include breathing difficulties, cramps and vomiting.

Some children go to school, as the law requires, but often only sporadically. Almost all work from sunrise in the fields before school and then when they get home, as well as through the weekend. At harvest time, classrooms empty.

BAT is one of the most profitable companies in the world, making an operating profit last year of £9.3bn on sales of £24.5bn. Like other big tobacco companies, it has distanced itself from the farmers by commissioning a separate company to buy a stipulated amount of tobacco leaf each year. Alliance One signs contracts with land-owning farmers in Malawi, who then recruit tenant farmer families to work the fields.

The lawyers, who have sent BAT the letter of claim and say they expect to issue proceedings this year, argue that responsibility for the conditions of the tenant families rests ultimately with BAT, which decides the price it will pay for tobacco leaf. In April, Leigh Day won a watershed case against Vedanta, a British mining company, which the supreme court ruled could be held responsible for the actions of its subsidiary in allegedly polluting farmland in Zambia. That case opened the way to hold other British companies responsible for harm caused by the actions of those who work for them overseas.

A report in 2011 estimated there were 1.3 million children under the age of 14 working in tobacco around the world. In 2017, an International Labour Organisation report said child labour in tobacco was on the increase and “rampant”.

Day said: “If we are successful in Malawi, I would very much hope it would persuade BAT and the other tobacco companies that use very similar models to change those models and make sure people are properly compensated for the work and totally discourage children from working so they can go to school.”

BAT said in a statement that it took the issue of child labour very seriously and “strongly agrees that children must never be exploited, exposed to danger or denied an education”.

Simon Cleverly, the group head of corporate affairs, said BAT’s core policies “specifically state that we do not condone forced, bonded or involuntary labour; and that we do not condone or employ child labour, and seek to ensure that the welfare, health and safety of children are paramount at all times”.

He said BAT made it clear to contract farmers and suppliers that exploitative child labour and forced and bonded labour would not be tolerated.

BAT leaf operations and contracted suppliers were required to participate in the industry-wide sustainable tobacco programme, he said, which was aligned with United Nations standards, including on child labour and income for farm workers.

“As we have received a letter of claim relating to these allegations, it would be inappropriate for us to provide further comment at this time,” Cleverly said.

• This article was amended on 6 November 2019 because an earlier version gave incorrect details of case concerning Vedanta and said it was in the high court. That ruling was in the supreme court.