Union bosses and Pontefract and Castleford MP Yvette Cooper are backing Asda workers who are being forced to sign new contracts which they says clamps down on breaks and working hours.
Ms Cooper joined the GMB at their regional office on Monday to discuss the situation.
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The global chain, whose roots can be traced to a butchers in Knottingley and a supermarket in Castleford, will offer an improved basic wage of £9 an hour, but with stringent conditions, including scrapping unpaid breaks and forcing employees to work bank holidays.
The concern led to Asda workers marching through Leeds last week.
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Ms Cooper said: “Asda started as a family business - first in Knottingley and then in Castleford. It’s only been successful across the country because of generations of hard-working staff.
“That’s why the way they are treating long standing Asda workers now is so unfair, and why the GMB Union are right to object.
!The new contract is a real problem for people with caring responsibilities who won’t be able to cope if Asda forces them to change their shifts at short notice.
“I’m calling on Asda to remember those Yorkshire family values and respect their workers now.”
But in a statement from Asda, they say they the move is an £80 million investment and that the majority of works have signed the contract.
A spokesman said: “The retail sector is undergoing significant change and it is important that we are able to keep pace.
“While we appreciate that some of our colleagues find the changes more unsettling, we do not want any of them to leave.
“We have been clear that we understand colleagues have commitments outside of work and will not be asking them to constantly move the time they work.”