Shabana Mahmood has announced plans to change modern slavery laws to prevent migrants from making last minute attempts to “frustrate a removal” after her bid to appeal in a trafficking case was thrown out by the court of appeal.

The home secretary had applied for permission to appeal against a high court ruling temporarily blocking the removal of an Eritrean asylum seeker to France under Labour’s “one in, one out” scheme so that he had more time to gather evidence in support of his trafficking claim. Three appeal court judges rejected her application.

“Last minute attempts to frustrate a removal are intolerable, and I will fight them at every step,” Mahmood said. “We have taken immediate steps to tackle this issue by amending policy on 17 September. I have also commissioned work to consider wider reforms and what more can be done to prevent misuse of the modern slavery system.

“I will fight to end vexatious, last minute challenges. I will robustly defend the British public’s priorities in any court. And I will do whatever it takes to secure our borders.”

The high court ruling last week granted the Eritrean man 14 days to gather further evidence in support of his trafficking claim before any removal could take place.

The court of appeal ruling on Tuesday against Mahmoud was made after judges heard arguments from the home secretary’s lawyers. After rising for a few minutes, the judges returned to court and said it was not necessary to hear arguments from lawyers representing the Eritrean asylum seeker before reaching their decision to reject the home secretary’s application.

The Eritrean man, who arrived in the UK on a small boat on 12 August, was due to be deported on an Air France flight to Paris last week, but Justice Sheldon delayed his removal in a high court ruling.

His lawyers had argued in the high court that he was entitled under UK trafficking rules to more time to gather evidence about his trafficking claim before being sent back to France.

Although the decision on Tuesday by the three appeal judges, Lord Justice Arnold, Lord Justice Lewis and Lady Justice Elisabeth Laing, does not jeopardise the Home Office’s controversial “one in, one out” scheme overall, it deals a significant blow to the home secretary, Shabana Mahmood.

Under the deal, the UK can send back any migrant who crosses the Channel illegally in return for accepting the same number of migrants in France who have a valid asylum claim here.

Government lawyers put forward arguments that it was imperative to remove the Eritrean man, who cannot be named for legal reasons, as part of the scheme to prevent dangerous crossings. They said he could pursue his trafficking claim in France but this was rejected by the judges.

So far only three people have been removed to France under the new deal. The first people from France were due to arrive on Saturday but this has been delayed.

Kate Grange KC, for the home secretary, told the court of appeal on Tuesday that there was “considerable urgency” to make “one in, one out” work. She said the scheme was needed to break the business model of people-smuggling gangs.

Grange told the court: “Winter is coming. Over the next few weeks temperatures will drop and journeys will become more hazardous.

“We submit that the public interest in preventing and deterring these journeys could not be more serious or acute.”

Rejecting permission to appeal, Lord Justice Arnold said: “The judge made no error of law or principle making the decision he did. None of the four grounds of appeal are sufficiently arguable to have a realistic prospect of success.”