An online survey by TNS UK found 41 per cent of UK respondents backed remain, while 43 per cent wanted to leave and 16 per cent were undecided. It accounted for differential turnout, or groups of voters less likely to go to the polling station.
It comes as the government is increasing its campaign to secure an in vote on 23 June, with separate data showing that a low turnout could actually favour Leave.
"The support for remain looks to be softer than the support for leave and without this adjustment remain would have a three point lead over leave," Luke Taylor, head of social and political attitudes at TNS UK, said.
"Whether or not remain supporters turn out will therefore be critical in the outcome."
It's based on responses from 1,213 adults in the UK between 19th and 23rd May. The data was subsequently weighted to match population totals for factors such as age, sex, working status and 2015 General Election voting patterns.
Of the nine other European countries surveyed as part of the wider research, all thought that the UK should stay in the bloc.
France and Germany thought that the UK will vote to remain, while the Netherlands and the Czech Republic were less sure as an equal number believed it will leave.