Most Britons would vote for the UK to leave the European Union if the referendum was held right away, according to a new poll. Support for a Brexit among UK adults is now at 43%, up three percentage points from two weeks ago, while support for Vote Remain slipped four percentage points to 40%.

Immigration and EU bureaucracy were named by voters as the two most important issues on which they will base their decision when they vote on 23 June, the Observer/Opinium survey showed.

Opinium also released a second analysis of the polling data, designed to compensate for online polls' tendency to over-represent socially conservative respondents. Using this analysis, 43% of voters would chose to stay in the EU, 41% would vote to leave, and 14% said they did not know how they would vote.

The new poll comes after Brexit campaigners Boris Johnson and Michael Gove pledged to create an Australian-style points-based immigration system by 2020 if the Leave campaign was successful. Half of the 2,007 people polled said a Brexit would help better control immigration to the UK.

Fractious debate

Tory rebel Johnson reiterated his criticism of the EU in an interview with the Observer, saying that the single market only existed to benefit the rich and powerful.

"The impact of EU-enforced uncontrolled immigration to the UK – made worse by the euro crisis – has been to depress the wages of the low-paid, while fat cat FTSE-100 chiefs have seen their pay packets soar to 150 times the average pay of their workforce," the former London mayor said.

"It is time that liberals everywhere saw the EU for what it is – essentially a stitch-up between the very biggest corporations, their lobbyists and the commission to frame regulation in such a way as to keep out the competition, especially… from start-ups and innovators."

The in-fighting in the Tory ranks has grown increasingly fractious as the referendum edges closer, with Prime Minister David Cameron pointing to the economic dangers of a Brexit as reason enough to stay in the EU.

"Their argument is: 'Let's wreck the economy by leaving the single market in order to do it'. I'm going to make them pay for that," he told the Daily Mail.

"The idea that the world just gives you great trade access is nonsense on stilts. Boris wants us to be like America, so you'd be subject to WTO (World Trade Organisation) tariffs on cars, clothes, shoes.

"It's common sense: if you cut yourself off from your biggest market your economy will be poorer – and they know that."

The latest poll-of-polls of the EU referendum created by NatCen Social Research shows support for the Remain and Leave campaigns evenly split at 50%. The poll-of-polls is an average of six polls taken between 20 May and 3 June.