The announcement is lent particular significance by the Duke of Cambridge's role as president of the English Football Association.
She also said the Royal Family would not attend the World Cup, and the FA has now said its priority is the safety and security of fans, players and staff.
British Prime Minister Theresa May has ordered politicians and royals not to attend the World Cup after former Russian agent Sergei Skripal and his daughter were found unconscious after being exposed to a nerve agent.
Officials, apparently anticipating deteriorating relations between Britain and Russian Federation, warned that Britons should aware of the risk of "anti-British sentiment or harassment" arising from "heightened political tensions". Southgate said his side could suffer if England fans decide against travelling to the tournament.
'Attendance at sporting events is a matter for the sporting authorities - it's a matter for them'.
The governing body is within its right to exclude any nation that pulls out of a World Cup from future editions of the tournament. "As is standard practice, we will take all travel guidance from the Foreign and Commonwealth Office".
British Prime Minister Theresa May said on Monday that it was "highly likely" that Russian Federation was behind the attack and promised "extensive measures" against the country if an explanation was not provided.