A Court of Appeal judge has ordered the Home Office not to deport people to Jamaica on Tuesday unless they had access to a functioning, non-O2 Sim card on or before 3 February.
The order comes after lawyers argued some set to be deported from two detention centres could not get legal advice due to issues with an O2 mast.
The Home Office said it was "urgently asking the judge to reconsider".
Earlier, Labour's Diane Abbott said removing the detainees was "unfair".
But Home Secretary Priti Patel said many were guilty of "serious offences".
Ms Patel said every person on the flight had "received a custodial sentence of 12 months or more".
Therefore under legislation introduced by the Labour government in 2007, she said, "a deportation order must be made".
In a statement, the Home Office said: "The planned charter flight to Jamaica is specifically for deporting foreign national offenders.
"Those detained for removal include people convicted of manslaughter, rape, violent crime and dealing Class-A drugs.
"We are urgently asking the judge to reconsider their ruling and it would be inappropriate to comment further whilst legal proceedings are ongoing."
The government has faced pressure to suspend the flight until a report on the Windrush scandal has been published.
A leaked draft of the report said the government should consider ending the deportation of foreign-born offenders who came to the UK as children.
The flight to Kingston is due to leave early on 11 February and is expected to include a man who arrived in the UK at the age of five.
Speaking in the Commons, shadow home secretary Ms Abbott said: "Many of the proposed deportees came here as children and have no memory of Jamaica."
Bella Sankey, director of charity Detention Action, said she was "delighted" by the ruling adding that: "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 [Tuesday's] flight."
"We understand that this will apply to at least 56 people."
And Toufique Hossain, director of public law at Duncan Lewis - which is representing some of those scheduled to be deported - said: "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."
'I have no-one in Jamaica'
One of those who had been due to be deported on Tuesday is father-of-five Howard Ormsby.
He was jailed for 18 months after he was convicted of possession with intent to supply class A drugs and he was released in December.
"I came here at the age of 15 with my older sister and I've been here 18 years of my life," the 32-year-old said, speaking to the BBC's Victoria Derbyshire show from a detention centre at Harmondsworth, west London.
"I've never tried to deny the fact I've made a mistake, but everyone has a chance to right their wrongs.
"I have all my family here - I have no-one in Jamaica."