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A YouGov 'on-the-day poll' suggests 52% for Remain and 48% for Leave.
Gibraltar has voted to remain in the European Union.
The British Overseas Territory was the first of 382 counting areas to declare its result in the EU referendum.
Out of 20,172 votes - 19,322 (96%) voted to stay in the EU and 823 (4%) voted to leave.
ITV News results analysis suggests there is a 75% probability that Leave will win.
"Leave are doing better than we expected them to do than two or percentage points," our elections analyst Colin Rallings said.
Professor Jane Green said Remain need to do far better in upcoming results to stand a chance of winning.
He said smaller margins of victory and weaker turnout than expected in Scotland was having an impact.
ITV News predicts Leave will win the EU referendum.
"An extraordinary moment in British history," News At Ten host Tom Bradby said.
Latest ITV News reports
Analysis shows the 25-34 age group engaged in conversation about the EU referendum most on Facebook during the campaign.
The Leave campaign claims Hartlepool was a 'forgotten town' which lead to a massive 69.5 per cent vote to leave the EU.