Updated advice from the Foreign and Commonwealth Office highlights stadiums, fan zones, other venues broadcasting the tournament and transport hubs and links as potential targets for atrocities.
British counter-terrorism officers are playing “a key part” in planning against attacks that may target the tournament and a team from the UK has travelled to France and is working with police and intelligence services there to assess possible threats.
On Monday, officials in Ukraine revealed they had arrested a Frenchman who was apparently inspired by extremist right-wing beliefs to plot a series of bloody strikes in his homeland after buying an arsenal of weapons in an undercover sting.
Commander Dean Haydon, the head of Scotland Yard’s anti-terror squad, said: “As we approach the Euros, any operation such as that in any country is clearly a concern. As you would expect, we are working with the French and other local police and security and intelligence agencies across the world to properly understand is there a threat to the Euros.
“Certainly we have seen propaganda, Islamic State (IS) and potential talk of plots against the Euros, but we’re working with all those various different agencies to police and make the Euros a safe event and a safe games.
“We’re a key part of the planning. Although the ultimate policing of the event and the planning is for the French, we are all involved in properly trying to understand the threat, if there is one.”
The advice from the FCO was updated on Monday, although officials said this was not linked to the Ukrainian arrest.
It says: “During Euro 2016, stadiums, fan zones, venues broadcasting the tournament and transport hubs and links represent potential targets for terrorist attacks. You should be vigilant at all times, especially in areas hosting Euro 2016 events, and follow the advice of local French authorities.”
A police operation targeting 29 UK ports in the run-up to the tournament began on Monday, with trained spotters trying to detect football hooligans attempting to sneak out of the country. Currently 1,841 England fans and 86 Wales supporters are subject to banning orders that stop them travelling to the tournament.
Matches at Euro 2016 will be played across several stadia and there are a string of fan zones for thousands of supporters. Fan zones will also be set up in London, which will be policed “normally”, Mr Haydon said.
“The threat level in the UK remains at severe, so an attack is highly likely - that has not changed. If we see increased intelligence coming out of France or anywhere in the world that suggests there’s going to be an attack here then of course, through Cobra (emergency committee) and Government, we will review that threat level accordingly.
“There are different events taking place throughout London, there are fan zones, there are screens going up for people in crowded places and in parks to watch the football. Of course we’ve got a policing event around that.
“We are policing that as we would do normally and obviously keeping an eye on France.”
Prime Minister David Cameron chaired a meeting on Monday on preparations for the tournament.
A Foreign Office spokesman said: “We have updated the travel advice to provide further information for fans on the risk of terrorism in France as they start to travel for Euro 2016. This is consistent with the advice we have already issued for France and is not in response to a new or specific threat or yesterday’s arrest.
“The relevant UK authorities are in constant contact with the Euro 2016 organisers and local authorities. France has lots of experience of hosting large scale events and the authorities have undertaken extensive preparations for the tournament.”
A Downing Street spokeswoman said the French authorities “have got an extensive security operation in place, with 77,000 police and gendarmes, 10,000 military personnel and a similar amount of security guards”.
She added: “We are providing additional counter-terrorism and public order support to the French. That includes, for example, the deployment of additional police on trains into France and more UK Border Force outbound checks.”