Theresa May has paid tribute to the “strong and deep relationship” between France and the UK as President Macron began his first visit to Britain.
The prime minister said both leaders remained committed to the “Le Touquet” border agreement in Calais and had agreed extra security measures.
It comes as the UK announced an extra £44.5m to be spent on beefing up Channel border security.
She stressed co-operation was vital on economic matters, defence and security.
The £44m will be spent on fencing, CCTV and infrared detection technology in Calais and other border points.
Britain is also expected to commit to taking more migrants from Calais, especially unaccompanied children, the BBC understands.
The summit between Mrs May and Mr Macron, at the Royal Military Academy Sandhurst in Berkshire, also featured the first meeting of the heads of Britain and France’s five intelligence agencies, and is being attended by UK cabinet ministers and their French counterparts.
The BBC’s diplomatic correspondent James Robbins said that while Britain and France were heading in different directions as a result of Brexit, both governments were keen to show that they would continue to work closely together.
The border offer
During last year’s French election campaign, Mr Macron said he wanted to renegotiate or scrap the 2003 Le Touquet agreement, which established French border controls in Britain and UK controls in Calais.
The agreement means undocumented migrants barred from entering the UK stay in France – many in makeshift camps. Up to 700 migrants are in the area, despite the camp known as the “Jungle” having been dismantled in 2016.
The UK government is already thought to have spent over £100m on security in the area over the last three years, and officials said the number of illegal attempts to enter the UK fell from 80,000 in 2015 to just over 30,000 last year.
A UK government spokeswoman said the latest investment was “about investing in and enhancing the security of the UK border”.
Other “juxtaposed” border controls are in operation at Eurostar stations in France and Belgium.
Some Conservatives are not happy
Dover MP Charlie Elphicke told the BBC the UK should not be “footing the entire bill for the French border at Calais” after it leaves the EU.
Fellow backbencher Andrew Rosindell said: “It is their problem as much as it is ours and it should not be a situation where we keep funding France every time they demand more cash.
“I’m all for cooperation with our neighbours, with our friends in France but, at the end of the day, this is British money and it has to be used in a tangible way to benefit Britain.”
Summit mood music
Mrs May and Mr Macron had lunch at a gastro pub and then inspected a guard of honour from the Coldstream Guards, in the freezing rain, at the Royal Military Academy, Sandhurst, the venue for their talks.
Senior ministers Boris Johnson, Philip Hammond and Amber Rudd also endured a soaking as they looked on.
Speaking ahead of the summit, Mrs May said: “Today’s summit will underline that we remain committed to defending our people and upholding our values as liberal democracies in the face of any threat, whether at home or abroad.
“But our friendship has always gone far beyond defence and security and the scope of today’s discussions represents its broad and unique nature.”
Laurence Haim, a former adviser to Mr Macron told the BBC’s Newshour the French president likes Theresa May and speaks fluent English, but will want to make it clear to her that he will not give any ground over Brexit.
How the leaders shape up
By BBC diplomatic correspondent James Robbins
Britain and France carry much the same weight in global affairs. Both sit at the world’s most exclusive tables of power – the Security Council and the G7 – and the sizes of their populations and economies are broadly similar too.
But while President Macron commands France, including his parliament, after last year’s stunning electoral successes – the same cannot be said of Theresa May.
Sharp disagreements over the UK border with France are difficult to resolve. Mrs May has conceded extra money for border security in Calais – and has separately offered Chinook helicopters to move French troops more safely over Mali.
Mr Macron, meanwhile, has offered the loan of the Bayeux tapestry. But Brexit still threatens to overshadow all this bonhomie. When it comes to Europe, these two countries are pulling in radically different directions.
Other commitments being unveiled include the deployment of three RAF Chinook helicopters in Mali, where French forces are fighting Islamist militants, and France sending more troops to reinforce a British contingent in Estonia on Nato’s border with Russia.
Downing Street said the RAF Chinooks would offer a “niche capability”, providing logistical support for the French operation in Mali, but that Britain would not be committing combat troops.
Mr Macron is also expected to announce the loan of the Bayeux Tapestry for display in the UK.