Sports Direct, the retailer founded by billionaire Mike Ashley, is facing legal action from 250 workers excluded from a multimillion-pound bonus scheme because they were on zero-hours contracts.

Lawyers acting for the part-time staff, who worked at the high street chain between April 2008 and August last year, are preparing to file multiple claims for breach of contract at the high court.

The employees were excluded from a bonus scheme that paid out about £160m worth of shares to 2,000 "permanent" workers in 2013.

The claims, which have been gathered in partnership with workers' rights group Pay Justice, could amount to a £4m-plus bill for Sports Direct.

The retailer has been widely criticised for employing nearly 90% of its staff on zero-hours contracts, which do not guarantee a minimum number of working hours a week and also fail to provide for annual leave and sick pay.

Elizabeth George of law firm Leigh Day, which will lead the claims, said: "These are the staff whose hard work over many years has brought about the record profits that funded the bonus awards in the first place. It's plainly unfair that they should have missed out.

"We believe that they had a contractual right to the bonus because regardless of the zero-hours label that the company has given their contracts they were all permanent employees of the company for the necessary number of years."

Many of those taking part in the action continue to be employed by Sports Direct. Pay Justice is encouraging any other staff who believe they might be eligible to make contact via its website.

"We are very pleased with the numbers that have come forward and we would be very keen for others to join them," said Paul Robertson from Pay Justice.

Sports Direct is already facing legal action in relation to its use of the controversial contracts. In November an employment tribunal will hear a claim by former employee Zahera Gabriel-Abraham. She says she left the retailer's Croydon branch in July last year after suffering panic attacks, which she blames on a lack of financial security as her contract offered no guaranteed work or income.

That claim, financially supported by more than 5,000 members of the campaign group 38 Degrees, will argue that part-time staff, nearly all of whom are on zero-hours contracts, are treated less favourably than full-time employees. Lawyers will also argue that the policy discriminates against women, who are more likely to work part-time.

The latest court action emerged as Sports Direct held its annual shareholders meeting at its headquarters in Shirebrook, Derbyshire. Chairman Keith Hellawell told shareholders he could not comment on zero-hours contracts for legal reasons.

He was responding to Rebecca Hay, a shareholder and activist from ShareAction, who had asked whether Sports Direct intended to "amend its contracts for zero-hours staff to exclude all clauses that restrict staff from working elsewhere or seeking permission to do so?"

The business secretary, Vince Cable, has warned "unscrupulous employers" he plans to ban clauses in zero-hours contracts that prevent workers from accepting shifts with more than one employer.

Hellawell told an almost empty room with just seven shareholders in attendance: "We always comply with government proposals or regulations."

However, he said he could not confirm the number of staff Sports Direct employed on zero-hours deals and had been advised by lawyers not to answer any questions relating to the contracts until after the tribunal was concluded this winter.

Sports Direct has credited its bonus scheme, which handed generous payouts to eligible workers, for helping it achieve strong sales growth during a tough time for retailers and halving the rate at which workers leave the company.

A second bonus scheme is due to pay out to about 3,000 employees next year and again in 2017, while a third scheme has been approved by shareholders.

Sports Direct shares slid nearly 2% on Wednesday as the company revealed that a 12% rise in group sales had been offset by a fall in profit margins in the three months to the end of July. Profits for the period rose 12% – slightly behind the City's hopes.

Dave Forsey, chief executive of Sports Direct, said trading had been hit by England's poor World Cup performance.