Campaigners believe the planned deportation to Jamaica of more than 50 people cannot go ahead after a Court of Appeal ruling.
The Home Office has been told not to remove anyone scheduled to be deported from two detention centres near Heathrow airport unless they had access to a functioning, non-O2 Sim card on or before February 3.
Lady Justice Simler granted the order without a court hearing following an urgent application on paper.
The charity Detention Action, which made the appeal, argued that some of the detainees at Colnbrooke and Harmondsworth detention centres were being denied access to justice.
It argued those being held do not have a functioning mobile phone, following issues with an O2 phone mast in the area, and did not have adequate access to legal advice.
The charity said it believed 56 people would be affected by the ruling.
Bella Sankey, director of Detention Action, said: “We are delighted with this landmark decision which is a victory for access to justice, fairness and the rule of law.
“On the basis of this order from our Court of Appeal we do not believe that anyone currently detained at the Heathrow detention centres can be removed on tomorrow’s flight.
“We understand that this will apply to at least 56 people.”
Toufique Hossain, director of public law at Duncan Lewis, which is representing some of those scheduled to be deported, said: “For weeks now detainees’ complaints have fallen on deaf ears.
“Their removal looms large, hours away and yet again it takes judicial intervention to make the Home Office take basic, humane and fair steps to allow people to enjoy their constitutional right to access justice.”
Liberal Democrat home affairs spokeswoman Christine Jardine said: “What will it take for this government to learn? Even after the appalling Windrush scandal, Conservative ministers were brazenly defending their plans to deport people just hours before the court ruled it unlawful.
“These deportation flights must stop until the Government has published the Windrush Lessons Learned Review in full.
“No-one can trust the Home Office to get these decisions right, and we owe it to the victims of the Windrush Scandal to prevent anything like it from happening again.”
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