Labour has called for a total review of the government's so-called "hostile environment" policy after ministers said part of it had been paused.
Data-sharing aimed at identifying illegal migrants has been suspended for three months so people from the Windrush generation were not "erroneously impacted".
The government has already apologised over the Windrush saga.
But shadow home secretary Diane Abbott said wider measures were needed.
"Unless we review it in detail, the Windrush generation will not be the last end of it in terms of unfairness and cruelty," she said.
On Wednesday, Home Secretary Sajid Javid revealed that pro-active data sharing between the Home Office and other departments had been paused for people of all nationalities over 30-years-old.
This was part of what has been called the "hostile environment" approach to curbing illegal immigration which has been blamed for members of the Windrush generation, who are in the UK legally, being wrongly threatened with deportation.
In the House of Commons, Labour MP David Lammy - who has campaigned on Windrush - accused the government of "slipping out" the announcement during England's World Cup semi final football clash with Croatia.
He called for more information on a "hardship scheme" and an appeal system for those affected.
"When she says pause, why not scrap this hostile environment which is bringing this country into disrepute," he said.
Immigration Minister Caroline Nokes said data sharing had been paused since April, under the tenure of former home secretary Amber Rudd, and would not be restarted until she was confident the Windrush generation would not be affected.
She said what the government is calling "compliant environment" policies had started under the previous Labour government.