An ORB poll for the Daily Telegraph found support for "Remain" at 53 per cent, up 5 percentage points on the previous one, with support for "Leave" on 46 per cent, down three points.
"All the signs of ORB's latest and final poll point to a referendum that will truly come down to the wire," said Lynton Crosby, a political strategist who advised the ruling Conservative Party at the last national election in 2015.
The Leave camp had "failed to quash the almost ubiquitous perception that it is the riskier of the two options", he said.
Respected social research body NatCen also published a poll that found Remain on 53 per cent and Leave on 47 per cent, using a method that took on recommendations by an official inquiry into why pollsters got last year's election wrong and conducted from May 16 to June 12.
However, an online poll by YouGov for The Times showed Leave ahead on 44 per cent, up one point, with Remain on 42 per cent, down two points. That survey was conducted over the weekend after Cox was killed.
Jeremy Corbyn, leader of the Labour Party, said her murder was likely "extreme political violence".
Those wishing to stay in the bloc, including Prime Minister David Cameron, have focused on what they describe as the economic advantages provided by EU membership and the risks posed by leaving.
Those arguing to quit have focused on what they say are pressures on public services and jobs created by high immigration levels that cannot be reduced due to EU freedom of movement rules.
Harry Potter author JK Rowling yesterday made an impassioned plea or Britons to vote to stay in the EU, warning in a blog posting against rising nationalism across the world.
Music producer Brian Eno took to social media at the weekend, saying: "I have a lot of misgivings about the way the EU is run, but they don't make me want to ditch the whole idea. I feel the EU is one of the only restraints on the kind of neo-liberal market fundamentalism that has seen inequality rising throughout the world."
Nearly 300 British actors, musicians and writers-including Benedict Cumberbatch, Danny Boyle and John le Carre-recently signed an open letter urging Britons to vote to stay, saying EU membership results in a "more imaginative and more creative" Britain.
- Reuters