The man, who cannot be named for legal reasons, is bringing a legal claim against the Home Office, asking the court for a block on his removal.
He was due to be on a flight to France at 9am on Wednesday.
The Home Office defended the case, saying that it was reasonable to expect the man to claim asylum in France.
On Tuesday evening, Justice Sheldon said: “I am going to grant a short period of interim relief.”
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The judgment came after a decision from the national referral mechanism (NRM) – which identifies and assesses victims of slavery and human trafficking – and the invitation from the NRM for the man to make further representations.
Ministers agreed the pilot scheme with the French government in July as part of efforts to deter the record number of arrivals by small boat crossings so far this year.
The first detentions of migrants took place last month as the deal came into force and they have been held at an immigration removal centre pending their removal from the country.
Under the arrangement, the UK will send back to France asylum seekers who have crossed the Channel, in exchange for those who apply and are approved to come to Britain.
Despite the ongoing legal challenge, Downing Street insisted it expects deportations to begin “imminently”, with the Prime Minister’s official spokesperson saying “for obvious reasons we’re not going to get into a running commentary on operational details before that”.
Sonali Naik KC, for the unnamed man, told the court on Tuesday the man faces a “real risk of destitution” if he is put on a flight to France.
Naik KC said there is “a serious issue to be tried” about whether or not the man would be destitute if returned to France.
The barrister continued: “We are not dealing with a charter flight, it is simply a postponement.”
Naik told the court the case “concerns a trafficking claim” and that her client, who alleges he has a gunshot wound in his leg, claims he is vulnerable.
The court heard that about a third of asylum seekers in France are not accommodated, and they are given a daily allowance of 7.50 euros.
Kate Grange KC, for the Home Office, said in written submissions that the man travelled to Italy in April 2025, before travelling to France and arriving in the UK in August 2025.
She continued: “The claimant asserts that he was destitute, but no less than two charities had indicated they would provide him with accommodation if he claimed asylum.
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“It is no answer that the claimant had friends who had claimed asylum and were living on the street, or that he wasn’t sure how long accommodation was being offered.
“He could have claimed asylum.”
Grange continued that the agreement between the UK and France “pursues an important public objective”.
She added: “Serious injury and death, including of children, from small boat crossings in the English Channel is a grave social and political concern at the present time.”
Giving his ruling, Justice Sheldon said the court should make a decision that “preserves the status quo”.
He continued: “The status quo is that the claimant is currently in this country and has not been removed.
“So, I make an order that the claimant should not be removed tomorrow at 9am, but that this matter should come back to this court as soon as is reasonably practical in light of the further representations that the claimant … will make on his trafficking decision.”
In 2023, the Supreme Court ruled that then-Tory prime minister Rishi Sunak’s plan to deport asylum seekers to Rwanda was unlawful.
At the time, Robert Reed, president of the court said there were “substantial grounds” for believing that there was a risk of people sent to Rwanda being wrongly deported to their country of origin, where they might face such persecution.
