A contingent of Metropolitan Police officers, including counter-terrorism and public order specialists, have already been sent to support French police for the event which kicks off on Friday.
"We have got to recognise that potentially [there] is a threat. But the important point to make is that the threat level is currently at severe and has not changed. It has been at that level for many years," said Commander Dean Haydon of Scotland Yard's counterterrorism unit.
Meanwhile, France has launched a "terror alert" smartphone app to warn people of attack threats during the month-long Euro 2016 championship.
The app, which is free to download in French and English, will send users a warning if the authorities suspect terrorists are about to strike.
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Paris remains under a state of emergency imposed after ISIS struck the French capital last November and then Belgium in March.
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Tens of thousands of football fans are expected to be drawn to watch the matches in parks, beaches, public squares, bars, pubs and other venues across Europe.
Over the weekend, it had emerged thatBritish special forces had been taking part in multi-national counter-terrorist operations to counter ISIS plots to attack London and other European cities during thefootball championship.
Operation Storm Tide 3 took place recently at Ostend in Belgium where troops stormed a shopping centre and "eliminated" a group of soldiers playing the part of extremists threatening to blow up the building as part of the training exercises.