Sports Direct is facing a claim for millions of pounds from nearly 300 workers excluded from the retailer’s generous bonus scheme because they were on zero-hours contracts.

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

Lawyers acting for the part-time staff sent letters to Sports Direct’s legal team on Friday claiming a total of just over £1m in compensation for missed bonuses for a first batch of 30 workers. The individual claims average about £36,000 each but the highest is worth more than £100,000.

All of the first 30 seeking compensation, with help from the legal firm Leigh Day, have a minimum of five and a half years in continuous employment with Sports Direct, including the period covered by the bonus.

Some of the staff involved, whose claims were gathered in partnership with workers rights group Pay Justice, have worked for the company for considerably longer, despite being employed on insecure contracts.

Letters relating to the remaining 268 workers will be gradually filed over the next six months or so. It is not clear if the average claim for all those workers will be £36,000 but, if it is, the total cost to Sports Direct could amount to nearly £10m.

Some of the workers making claims for the missed bonuses still work for Sports Direct, and Leigh Day has called on the company to confirm they will not be penalised or dismissed for making the claims. The law firm says that to do so would be unlawful under regulations that protect part-time workers.

On receiving the claim letters, Sports Direct is required to provide a response. If the two sides cannot reach an agreement, the claims will go to court, which will then have to determine whether the long-serving, zero-hours staff had a contractual right to the bonus awards and should therefore be compensated.

Sports Direct, which is controlled by the billionaire Newcastle United football club owner Mike Ashley, has been widely criticised for employing nearly 90% of its staff on zero-hours contracts.

In October last year, the retailer was forced to make clear the limitations of such contracts to staff and to inform them that they were entitled to sick pay and holiday pay after legal action by former worker Zahera Gabriel-Abraham.

Gabriel-Abraham left the retailer’s Croydon branch in 2013 after suffering panic attacks, which she blamed on a lack of financial security as her contract offered no guaranteed work or income. Her legal action was backed by the financial support of more than 5,000 members of the campaign group 38 Degrees.

Sports Direct said the settlement was made without admission of any liability whatsoever.

Lawyers said the public nature of the company’s promise to communicate more clearly about zero-hours contracts with staff meant it could be held to account.

The latest legal action highlights how zero-hours workers, many of whom have worked for the company for long periods of time, have been excluded from Sports Direct’s generous staff bonus scheme.

The company has credited the payouts for helping it achieve strong sales growth and halving the rate at which workers leave the company.

A second bonus scheme is due to pay out to about 3,000 employees this summer and again in 2017.

In July last year, shareholders passed a third bonus plan that would hand 25m free shares in the company to about the same number of “permanent” staff, including Ashley, if earnings double by 2019. Ashley pulled out of the scheme a few days later.

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

Cable launched a review in October that he said would ensure employers knew their responsibilities and individuals their rights. Sports Direct declined to comment.