MPs have called on Sports Direct to end its relationship with Transline, which supplies workers for the retailer’s Shirebrook warehouse, over fears that the employment agency misled a parliamentary inquiry.

Iain Wright, Labour MP and chair of the Commons business, innovation and skills (BIS) select committee, which published a damning report on Sports Direct in July, has written to the retailer’s founder and majority shareholder Mike Ashley saying he believed Transline was not candid about the reasons for its lack of an operating licence from the industry watchdog.

The BIS committee has also warned Transline that it is considering reporting to the Commons that the company’s directors are not fit to run the company because of concerns about its dealings with Gangmasters Licensing Authority (GLA).

“We ask you to think seriously about continuing to use Transline, a company that treats their workers and conducts its business in a way that is inconsistent with your own aspirations for Sports Direct to be on a par with likes of Selfridges and John Lewis,” Wright wrote to Ashley, in a letter published by the BIS committee on Tuesday.

He added that Sports Direct not having any formal written contract with Transline – as revealed in a report by the retailer’s lawyers published last week – “could make any decision to terminate the working relationship with Transline somewhat easier”.

A spokesman for Sports Direct said: “We have received a letter from the BIS Committee and we will give careful consideration to the contents of the ongoing correspondence. We will not be making further comment at this stage.”

The BIS committee report published in July raised concerns about employment conditions at Sports Direct’s Shirebrook warehouse, where most staff are employed through Transline and one other agency, The Best Connection.

The parliamentary inquiry, which followed an undercover investigation by the Guardian into working conditions at Shirebrook, questioned the legality and fairness of voluntary schemes provided by the agencies to workers such as pre-paid debit cards and insurance services.

Since then, Sports Direct and its employment agencies have been forced to award about £1m in back pay to Shirebrook warehouse staff found to be have been paid less than the national minimum wage.

The committee has asked Transline to confirm if its licence was refused by the GLA because directors were found not to be “fit and proper persons” and to reply by 16 September.

The letter says Transline did not acknowledge that it traded without a licence between July and September 2013. It adds that the GLA refused Transline’s application because it had found examples of the company not paying the minimum wage and not paying workers for time spent on inductions.

The letter added that Transline did not mention that it had a second application, under a different company name, for a licence refused partly because it had not been candid about the links between the two companies.

Transline has written to Wright saying it can see “absolutely no basis for the committee to state that we misled the committee in responding to the committee’s inaccurate assertion that the company’s GLA licence had been revoked”.

The company said the committee was biased against Transline and it was “astounded and extremely saddened” to read what it said were inaccurate critical comments about its operation and evidence.

It also pointed out that the GLA licensing system only related to the food industry and so had no bearing on its work with Sports Direct.

A Transline spokesperson said: “We have always provided accurate information to the select committee and are focused on supporting Sports Direct in reviewing and implementing recommendations and actions from the working practices report. We will continue to offer clarity and any further information necessary to the committee. Obviously we find Iain Wright MP’s statements and summary disappointing, however we will prioritise responding to the latest correspondence in a full and concise manner, within the requested timescale.”

Wright said: “We on the committee are very keen to see improvements to working practices at Sports Direct. Mike Ashley says he is committed to making conditions better for staff at Shirebrook. If he means what he says, he could start by cutting his ties with Transline Group who have not been candid or credible in their evidence to the business committee and, as we heard in our evidence sessions, have deducted money from low-paid workers without proper explanation and justification.

“I would expect other companies using Transline Group will want to think seriously about using a company that treats their workers and conducts its business in this way.

“Neither Mike Ashley nor the RPC report into working practices last week have explained why so many people at Shirebrook are employed through agencies, and why they are employed on short-term contracts, other than to reduce costs and avoid legal responsibility for their poor working conditions.”