The YouGov survey of 1,986 adults for the Times found 34% of those it questioned would back pulling Gareth Southgate’s team out of the finals in Russia this summer.
Some 39% rejected the idea and 27% said they were unsure, while among those who were football fans, 32% also favoured a boycott and 56% believed the team should take part.
Twelve percent of football fans said they were unsure.
MPs have raised questions over the national team’s participation, as well as concerns over the safety of the travelling fans, after former Soviet spy Sergei Skripal was poisoned with a nerve agent alongside his daughter two weeks ago.
The pair were discovered on a bench in Salisbury, Wilts, sparking a huge military response when it became clear dangerous chemicals were involved.
Prime Minister Theresa May joined the leaders of France, Germany and the US in blaming Russia for the attack.
And she stepped up pressure on the country by expelling 23 diplomats from Britain. Russia responded on Saturday by expelling the same number of UK officials from Moscow.
The 2018 World Cup is due to kick off in Moscow on June 14, and is expected to be used by Russian President Vladimir Putin as a massive PR opportunity for his country.
But Labour’s Stephen Kinnock suggested Britain should ask Fifa to postpone the tournament to 2019 and take it away from Russia in retaliation for the Salisbury poisoning.
His fellow Labour MP John Woodcock also called for Parliament to debate whether the Government should ask its allies to advocate postponing the summer championship or move it to another country.
The Barrow and Furness MP earlier said England’s participation “ought to be in question”, while Conservative chairman of the Commons Foreign Affairs Committee, Tom Tugendhat, raised fears football fans travelling to the country for the tournament may be at risk of harm if tensions escalate between London and Moscow.
May has said no Government ministers or members of the Royal Family will attend and the Foreign Office has warned England fans planning to travel to Russia that they should “be aware of the possibility of anti-British sentiment or harassment”.
But the Press Association reported that the Government has not given its backing to a boycott of the tournament, insisting that the England team’s involvement is a matter for the Football Association.