Odds have consistently indicated a high probability of an "In" result in the June 23 referendum.
"There does seem to have been some move towards staying in the EU, particularly given that ours is an online methodology which typically shows a closer race than polls conducted on the phone," Adam Drummond of Opinium Research said.
Telephone polls have tended to show a larger lead for the "Remain" campaign, with online surveys instead suggesting the referendum result will be too close to call.
Opinium surveyed 2008 adults between May 17 and 19.
"The change comes mainly from Conservative voters who have moved from narrowly backing Brexit at the end of April to a large lead for remain," Drummond added.
- Reuters, AAP