A woman hands out leaflets campaigning to stay in Europe for the BREXIT vote in London, Britain, May 20, 2016. REUTERS/Kevin Coombs

(Reuters) - Britons are evenly split on whether the country should remain or leave the European Union, a YouGov poll showed on Wednesday, as the In campaign struggles with poor voter support for its leader Prime Minister David Cameron.

A YouGov poll for the Times newspaper put support for the Remain campaign at 41 percent, down 3 percentage points since last week, with support for Leave up 1 point on 41 percent.

Four percent of respondents said they would not vote while 13 percent still did not know which way they would go with less than a month until polling day.

The polls, which are being closely watched by financial markets for their ability to move the value of sterling, have been close in the run-up to the referendum, but the Remain camp had appeared to take a lead in the last 10 days.

An ICM poll released on Tuesday, however, showed the rival sides tied, and YouGov on Wednesday said the referendum was damaging trust in Cameron, after he warned about the risks to Britain’s economy and security if it votes to leave.

Asked who they trusted over Europe and the referendum, just 18 percent said they trusted Cameron, down 2 percent since YouGov asked the same question in early March.

The person most trusted was Boris Johnson, the former mayor of London who is leading the campaign to take Britain out of the 28-member bloc, who was trusted by 31 percent of respondents.

Britons will vote on June 23 in a historic referendum on whether to stay in the group the country joined in 1973. YouGov said its poll took place on May 23-24 but did not give any further details.