The French government said it was now "highly likely" public transport and tourist sites in the UK would be hit.
The warning followed revelations that a UK terror suspect killed in Pakistan was being groomed to lead a new group in raids on the UK, France and Germany.
On Sunday Britain raised its terror alert level from general to high for travellers to Germany and France.
But it left the UK threat level unchanged at "severe".
The fresh advice on France's defence ministry website says: "The British authorities consider that the terror threat level is very high in the United Kingdom and that the risk of an attack is highly likely.
"It is recommended to show extreme vigilance on public transport and at the most-visited tourist sites."
Splinter group
The new warnings came after British terror suspect Abdul Jabbar was killed in a drone attack in north-western Pakistan on 8 September.
The BBC's Newsnight said he was put forward as the head of an al-Qaeda splinter group tasked with carrying out Mumbai-style commando attacks in Britain, France and Germany.
Newsnight spoke to a "trusted, senior security source" overseas who said Jabbar intended to lead a group called the Islamic Army of Great Britain. Whitehall officials have declined to comment.
The programme said the security source confirmed Jabbar was a British citizen with a British wife, and was living in the Jhelum area of Punjab in Pakistan.
According to Newsnight, intelligence agencies monitored a meeting of 300 militants three months ago in the Ambarshaga area of North Waziristan, attended by Jabbar and militants from the Taliban and al-Qaeda.
Details of the plot first emerged in the US media, and the suspicions were confirmed by security sources to the BBC last month.
Newsnight's source said the intelligence led to the drone attacks on 8 September, in which Jabbar and three other militants were killed.
Western intelligence sources have said the plan in Europe was for small teams of militants to seize and kill hostages
They were to model their mission on the bloody attacks in the Indian city of Mumbai on 26 November 2008, which left 166 people dead.
The US, Sweden and Japan have also updated advice to citizens travelling to Europe.
France has urged citizens travelling to Britain to be "extremely vigilant" amid raised fears of a terror attack there.