Trade unions are lobbying City investors to put pressure on Amazon to improve conditions for its workers in the UK.

At a meeting at the TUC’s head office this month the GMB union made presentations, including one from an Amazon employee, to a dozen leading fund managers and pension funds that own stakes in Amazon including Legal & General, Baillie Gifford and Aberdeen Standard.

The meeting was organised by Trade Union Share Owners (Tuso), which forged a coalition with institutional investors in 2016 to force Sports Direct to set up an independent review of working practices.

The GMB told investors that workers at Amazon’s giant warehouses worked long shifts under pressure to hit targets for items picked, causing pain and injuries.

The Amazon worker’s allegations included lack of action on sexual harassment, unsafe working conditions and warehouse managers dismissing employees’ concerns and problems.

The union told investors the company’s refusal to change would leave it exposed as public opinion swung against the power of big companies. Risks include legal challenges to treatment of workers, a backlash against tax avoidance, a shortage of workers after Brexit and new union laws under a Labour government, the GMB said.

Neil Foster, a GMB national officer, told the meeting on 8 May: “We are in a volatile climate and Amazon is vulnerable on so many different angles. We want to work with Amazon and we think investors have a place in that conversation.”

Amazon, which has 17 warehouses in the UK and employs 27,500 workers in Britain, said: “These allegations are false and unsubstantiated. Amazon already offers industry-leading pay, comprehensive benefits and career growth opportunities, all while working in a safe, modern work environment. But you don’t have to take our word for it – anyone can come and see for themselves by booking a tour of a fulfilment centre online.”

The company said its employees worked a normal 40-hour week and that it was normal to have measures of performance. Amazon said it did not tolerate harassment in the workplace and that it would investigate the GMB’s claims if the union supplied the necessary information.

Amazon refuses to recognise unions and has faced long-running accusations of gruelling working conditions at warehouses in the UK and the US. Workers in the US have started organising towards forming a union and the UK investors heard from Uni Global Union about its push to organise Amazon workers in Europe.

Investors who attended the meeting said they took the presentations seriously, and some pledged to raise working conditions with Amazon. They discussed tactics for getting Amazon to change, including voting against individual directors.

One institutional investor familiar with the meeting said: “Company culture and human capital management are coming up more frequently in discussions with companies. We see it as a reputation issue. A company needs to be attractive for people to want to work there and to stay there and also to attract and retain customers, and we have seen huge backlashes against companies where customers have voted with their feet.”

Janet Williamson, Tuso’s chair, said the meeting was a first step in getting shareholder support for better working conditions at Amazon.

“Our aim was to introduce investors to working life at Amazon and enable them to hear for the first time from an Amazon worker about the reality of working at Amazon,” she said. “We will keep investors up to date with Amazon’s working practices in the UK and elsewhere and ask investors to raise these points with the company.”

At Amazon’s annual meeting on 22 May in Seattle the company will face a series of resolutions calling for reform of its governance and reviews of its impact on the environment and society. Investors will vote for a second year on splitting Jeff Bezos’s dual roles of chief executive and chairman after about 40% of independent shareholders voted for an independent chairman last year.

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The institutional investor said concerns about Amazon’s treatment of workers sat alongside wider questions about the company’s governance, including the dominance of Bezos, who is Amazon’s biggest shareholder and the world’s richest person with a fortune estimated at $151bn (£117bn).

“Independent oversight of a company is extremely important. Last year’s significant vote in favour of requesting the company has an independent chair was a huge indication that a large chunk of investors saw risk oversight at the very top as a problem,” the investor said. “One thing Amazon could do better is engage with its shareholders in a more transparent way.”

Amazon said it trained employees in safety from their first day and that Health and Safety Executive figures showed it had 40% fewer injuries than other transport and warehouse companies in the UK. The company said it encouraged employees to take comments, questions and concerns to their managers.