Killings at a British-owned gold mine in east Africa have alarmed a group of MPs, lawyers and human rights campaigners, who have called on the British government to intervene.

The all-party parliamentary group on international corporate responsibility met last week to discuss incidents at a Tanzanian mine run by African Barrick Gold (ABG), amid unconfirmed allegations that four people may have been killed there this year.

Lisa Nandy MP, who chairs the group, said: "In the past six years we know that 16 people have been shot dead by the Tanzanian police, which indicates that this is a major problem."

The British firm is a subsidiary of Toronto-based Barrick Gold Corp and has been embroiled in years of controversy over how it handles security at North Mara, an open-pit gold mine in the far north of Tanzania.

It sits in the middle of a group of seven villages, which are home to 70,000 people, most of whom live in poverty and prospect for specks of the precious metal in the waste dumps and pits of the mine as a way of survival.

Villagers, including one man who has been left disabled and the relatives of six men who were killed, are suing ABG in the UK high court, represented by British law firm Leigh Day, alleging that Tanzanian police officers shot unarmed locals. The claimants say the company is responsible because the police are an integral part of the mine's security.

Last year ABG paid compensation to 14 women who were sexually assaulted by police and security guards at the mine.

Shanta Martin, a partner at Leigh Day, said: "The numbers who have been shot and injured on the mine is just extraordinary. In 2014 we should be sending the message to all that there is no place to hide if you violate human rights. We would expect any British company to operate to the same standards in the most remote corner of the world as they would do operating in the UK. The mine's own security are not armed with live ammunition; they have teargas and non-live projectiles. But they are commonly accompanied by police who do carry live ammunition, and use it."

Tricia Feeney, executive director at human rights group Rights and Accountability in Development (Raid), which has called on ABG investors to question the death toll at the mine, told the meeting: "The human rights record of Tanzania is astonishingly bad. No one should rely on Tanzanian police to enforce security. The British government has signed up to protect human rights, so why doesn't it incentivise good behaviour? They are not taking this seriously at all."

She said that every day, hundreds of men and women continued to go to the mine to collect rocks that they hoped contained tiny amounts of gold, something locals had done since before the open mine was established in the area. She rejected ABG's recent adoption of a voluntary code of practice and assurances it was taking allegations seriously. "I can't see any major change in the way it deals with this problem," she said.

Lisa Nandy, who chairs the parliamentary group on corporate responsibility, said the North Mara mine had 'a major problem'. Photograph: Martin Argles for the Guardian

A representative of ABG told the Observer that the company had not been able to attend the meeting at Westminster, having been invited only the day before it took place. He said ABG was keen to arrange a meeting between the all-party group and chief executive Brad Gordon, who has been credited with trying to address community tensions.

"African Barrick Gold is vigorously defending itself against Leigh Day's lawsuit, which currently involves 10 claimants," the spokesman said. "We are deeply saddened by any injury or loss of life at our operations. The company is committed to addressing legitimate grievances in an open and transparent way, but we will not compensate illegitimate claims or lawsuits."

He added: "While some local people conduct legitimate artisanal mining in areas near North Mara, of greater concern is highly organised trespass on to the mine site. This often involves hundreds or even thousands of illegal, armed and violent intruders systematically stealing gold-bearing rocks and other property from the mine. In 2013, there was a 35% reduction in the number of illegal miners on site compared with 2012. This reduction follows five years of consecutive increases in the number of intruders on site.

"As a company, we are committed to ensuring that all precautionary measures are taken in order to prevent any incidents between intruders and the police. It is only in very rare cases and extreme circumstances and when all alternatives have been exhausted that the police intervene in confrontation with intruders. We regret any loss of life at the mine and continually strive to improve relations with local community members to reduce instances of trespass.

"In addition to community investments, we have continued to train our staff to ensure they are prepared and equipped to manage situations that arise whilst ensuring we fully comply with the UN voluntary principles on security and human rights," he said.

To date, 31 men and 24 women have accepted remedy packages in response to grievances involving allegations regarding the use of force by mine security or police against intruders.