The controversial move is part of the new multimillion pound deal signed by Theresa May and French president Emmanuel Macron at Sandhurst Military Academy, Berkshire, during his first visit to the UK.
Mr Macron said the time to process adults’ applications would be cut from six months to one month, with the processing of unaccompanied children cut to 25 days.
And he repeatedly vowed that Britain’s decision to leave the European Union would not impact on close Anglo-French relations.
But he insisted Britain could not expect the City to keep its free access to the EU single market unless it contributed to EU budgets and abided by all the bloc’s rules.
On border control, the two leaders signed a new Sandhurst Treaty, designed to reform and improve how they manage the border in France.
Britain had already alarmed Eurosceptics by saying it would pay another £44.5million to boost fences, CCTV and infrared detection technology in ports along the Channel, where officials from both countries jointly administer the Anglo-French border.
Mr Macron stressed the new treaty would “enable us both to have a more humane approach to these people and to be more efficient” while, also protecting and encouraging vital trade through the Channel ports.
Government sources insisted it was not about increasing the number of immigrants coming to Britain.
Quicker processing would enable those with unjustified claims to be sent back quickly to their home countries, officials stressed, while it could also reduce the “pull factor” attracting migrants to Calais, if they knew they could be quickly turned back.
Britain has already committed to accepting 480 lone child refugees from the Continent and Mrs May strongly defended the new deal, insisting: “This is in our national interest. It is also in the interest of France to ensure we have as secure a border as possible in Calais and other ports.
“It’s about protecting our national interest and ensuring we have that much more secure border.”
In a joint press conference after a summit with Mrs May, Mr Macron hailed new co-operation deals, including on defence where the UK will aid French anti-terror operations in Mali and France will continue aiding the British-led Nato force in Estonia against Russian aggression.
Pointing to his country’s agreement to lend Britain the 950-year-old Bayeux Tapestry in 2022, he said he hoped the gesture would be the start of a new era of cultural and scientific links between the two countries, “so we are somehow making a new tapestry together”.
But he stressed the EU 27 were negotiating Brexit with Britain through their single negotiator Michel Barnier, and that the City of London could not expect special access to the EU single market after Brexit without many more concessions by Britain.
“If you want access to the single market – including the financial services – be my guest. But it means that you need to contribute to the budget and acknowledge European jurisdiction,” he said.
Mrs May said it was in the interests of all sides to have a trade deal that covered both goods and services.
But she said: “We recognise that as we leave the EU we will no longer be full members of the single market.”
She continued: “I think the City of London will continue to be a major global financial centre.
“That is an advantage not just for the United Kingdom, it’s actually good for Europe and good for the global financial system.”