The measure was one of a number announced by British Prime Minister Theresa May on Tuesday in response to the March 4 poisoning of Sergei Skripal and his daughter in England.
May said her government had found that Russia was "culpable" of the attack -- a charge Moscow angrily denies.
"It is every fan's choice, whether to come or not," Russia's World Cup organising committee chief Alexei Sorokin told the RIA Novosti state news agency.
"It will have no impact on the quality of the tournament. We still intend to organise it at the highest level," said Sorokin.
The possibility of an English team boycotting the first World Cup staged in Russia has been heavily analysed by the Moscow press and irritated football officials.
Moscow's Sport Express newspaper ran a story ahead of May's announcement warning in a headline that "sport is being taken hostage".
Travelling Britons warned
May's announcement should remove the worst-case scenario -- an English boycott -- for Russian organisers and the world football governing body FIFA.
But Sorokin still criticised May for giving a diplomatic snub to a tournament that has been associated closely with Vladimir Putin since the Russian strongman wrested the hosting rights away from England in 2010.
"It is a shame that not everyone adheres to the principle of football being outside politics," Sorokin said.
England faced a possible ban from the 2022 tournament in Qatar if it missed this year's event.
May unveiled a raft of reprisal steps for the poisoning that included expelling 23 Russian diplomats and suspending high-level diplomatic contacts with Moscow.
"There will be no attendance by ministers -- or indeed members of the royal family -- at this summer's World Cup in Russia," May told lawmakers.
The Foreign Office also warned Britons currently in or travelling to Russia of a risk of "anti-British sentiment or harassment".
Most foreign fans attending the June 14 to July 15 competition will be arriving in Moscow before either flying or taking a train to one of the 10 other host cities.
England will play their opening match against Tunisia on June 18 in the Volga River city of Volgograd.
They travel up the river for a June 24 encounter in Nizhny Novgorod against Panama before wrapping up their group stage games against Belgium on June 30 in the western exclave of Kaliningrad.
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