
Foreign Secretary Yvette Cooper defended the migrant returns deal with France as the number of arrivals since the scheme was introduced surged towards 10,000.
Just 26 people have been deported to Paris since Keir Starmer's one-in, one-out deal with Emmanuel Macron came into force on August 7.
Ms Cooper said there was "huge potential" for deportations to increase under the scheme, the aim of which in its pilot stage is to "get things going".
"With the pilot now being rolled out, now, we have the potential to be able to ramp it up," she told LBC.
"I do want to see those numbers increase. I also want to see that be built with other countries as well. We do have to test processes and deliver it.
"If you remember, the previous government ran a Rwanda scheme that ran for two-and-a-half years, didn't return a single person."
Ms Cooper, who worked closely on implementing the UK-French deal in her previous brief as home secretary, told BBC Breakfast: "It's a pilot phase, but that has huge potential, because that is returning for the first time people who arrive on small boats... where the boats set off from.
"That was something that was never possible under the previous government."
Some 35,503 people have crossed the English Channel in small boats so far this year, 33% higher than at this point in 2024.
And an ally of the French interior minister Bruno Retailleau, Xavier Bertrand, said France should stand by and let migrants freely cross the Channel to "scare" Labour into taking action.
The president of the Hauts-de-France region claimed Paris is "guarding the border" for Britain.
And he said the UK is responsible for the small boats crisis alongside the people smugglers.
Despite Britain agreeing to hand over more than £660m to stop migrants leaving their shores, Mr Bertrand claimed "we're practically forced to beg them to give us part of the cheque they owe us".
In fresh incendiary comments, the French politician declared: "We should tell the Border Force, 'This week, stay at home, we don't want to see you and we're going to let everyone through.
"Then you'll see what happens: the English will get scared, and in two days they'll sit down at the table with proposals to change things. Right now, we're practically forced to beg them to give us part of the cheque they owe us simply because we're guarding the border for them. That's enough.
"Let the migrants through. My proposal isn't very clever. But it's the only one that can change things."
More than 35,000 migrants have crossed the Channel so far this year, despite a one-in-one-out returns deal being agreed between London and Paris.
And more than 20 people have died attempting to reach the UK in a small boat.
But Mr Bertrand bizarrely claimed France was indifferent to the fact that "people are dying every week", adding: "Very clearly, we know who is primarily responsible: the smugglers, the criminals who exploit these networks.
"The second party responsible is the British. Because there wouldn't be these deaths, there wouldn't be hundreds of people trying to cross every week, if they didn't have jobs in Britain."
Mr Bertrand said he held Britain, along with people-smugglers, responsible for deaths in the Channel because of the UK's "hypocrisy" over its stance on the black market economy.
He said: "The British say, 'now we're going to set up a legal immigration channel. That means we're going to accept them legally and then send them back to France'."
Mr Bertrand, who has backed Interior Minister Bruno Retailleau's potential Presidential bid in 2027, also slammed Keir Starmer's one-in, one-out deal.
He said: "Of course, it can't work. We'll just end up having two channels, one illegal and one legal."

It comes as fury erupted over the Taliban seemingly selling fake death threat documents for as little as £40 to allow migrants to game the Home Office.
Corrupt officials in Afghanistan produce government letters threatening to kill asylum seekers. The letters are then used as evidence in asylum applications.
They include warnings that the Taliban will "deliver justice upon you" - shorthand for execution - for co-operating with the "evil government of England".
One letter says: "The mujahideen monitor all your activity on social media and will deliver justice when they see you. God will be pleased and you will be freed from this shameful life."
Shadow Home Office minister Katie Lam said: "When asylum seekers are openly boasting about using death threats to game the asylum system, serious questions must be asked of the Home Office, starting with how many forgeries have been detected in asylum applications.
"If the department can be duped so easily, it is no wonder thousands are crossing the Channel unchecked, in hopes of launching an asylum claim as soon as they arrive.
"Every day ministers refuse to act, our border security is weakened. Anyone who comes here illegally should be detained and swiftly removed, either to their own country or a safe third country. This government talks tough but delivers nothing, and the British public are paying the price."
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