Contracts used at fashion firm Asos's warehouse are exploitative and need to "be tested in a court", the head of the Commons business committee has said.
MP Iain Wright told the BBC that Parliament should examine "flex" contracts, which allow some shifts to be extended by two hours or reduced.
An employment lawyer said the contracts could breach employment legislation.
XPO Logistics, which runs the warehouse on behalf of Asos, said it was "fully compliant with employment law".
But the company has told workers it is making changes to some of its practices.
Asos is one of the UK's biggest online fashion retailers and has more than nine million customers.
Its warehouse in Grimethorpe, near Barnsley, employs about 4,000 workers, with those asked to "pick" items for distribution given a target of 160 items an hour, while the "pack" target is 170 items.
Many of the staff who spoke to the BBC complained about the "flexing" clause, which operates on alternate weeks and is designed to cope with peak times and quiet periods.
Emma Clark, a former team leader and single parent, said she struggled to find childcare when asked to "flex up" just before a shift.
"I don't drive - I'm reliant on public transport. The childminder couldn't always do it."
She would sometimes have to take a taxi to her sister's house to drop her young daughter off.
She said if she refused to flex up because of childcare commitments, she would be disciplined.
"They'd say that I'd go down as a late anyway. It would go against my review."
Another worker, who asked not to be named, said she had been asked to do extra hours in the middle of a shift.
"I'd describe it as unpaid overtime. If we don't do it, we're disciplined. I've been up for disciplinaries for refusing to flex."
A third worker said they had been flexed up at every opportunity in June and July, and were now owed payment or time off in lieu for 60 hours.
Since our investigation began, workers have been told they will no longer be flexed up on the day.
Staff have now been promised that all outstanding hours in the "flex" bank will be paid this month and in future unpaid "flex" hours will be settled at time and a half at the end of the financial year.
In a response to our questions, XPO said staff were informed of "flex" shifts in February for the following financial year and it encouraged staff "struggling with childcare arrangements to raise any issues".
The company said staff had only been asked to flex up on the day of their shift three times since April.
It said flex bank hours were offset as soon as was "reasonably possible" and workers could now request to be flexed down.
It said that "persistent non-attendance for flex hours may result in disciplinary action" but no-one had been sacked "as a result of a failure to attend a 'flex' shift".
It added that employees were paid the same amount each month, irrespective of whether they worked more or less than their contracted hours.
This practice is known as an "annualised contract".
But employment lawyer Zoe Lagadec said it meant the company could be breaching employment legislation.
She believes the additional hours worked should be regarded as part of a "time work" contract, which legally requires payments within 31 days.
"They should be reconciled during the National Minimum Wage reference period which can't go beyond a month."
XPO said all employees were paid "no less than the National Minimum Wage" and it was "fully compliant with employment law".
Iain Wright, who chairs the Commons Business, Innovations and Skills Select Committee, said flex contracts needed to be examined over their legality.
"They need to be tested in a court of law in terms of whether the legal process is robust enough.
"If I'm a manager and asking you to flex up and giving you a notice period of minutes or hours and then not reconciling the work done and the pay given for something like 10 or 11 months, that's exploitation, that's abuse."
He said he wanted to question company bosses over flex contracts.
"I also want government to answer that question - how is that allowed in law? And whether Parliament now has to change the law to address that."
The GMB union, which represents workers at the Grimethorpe warehouse, has called on Asos to do "far better" to address concerns over working practices at the site.
Regional secretary Neil Derrick said: "This is about respect and dignity for workers. These are our people, not machines.
"Our battle to defend our members' rights in Barnsley has got this company on the ropes.
"The end to same-day flex arrangements and prolonged probation periods this week are significant U-turns and a testament to our hard fought union campaign.
"But this does not end here - our members deserve far better than this."
In a statement, Asos said it cared deeply about its staff and provided learning and development programmes and free mental health support inside the warehouse.
Do you have a story you would like BBC News to investigate? Email firstname.lastname@example.org with your views and experiences. Please include a contact number if you are willing to speak to a BBC journalist.