The leave campaign has picked up momentum and taken a three-point lead over remain in the latest Observer/Opinium poll on the EU referendum. The Brexiters now stand on 43%, while 40% say they support the campaign to keep the UK in the union.

The poll suggests the remain camp has lost four percentage points in the last two weeks, during which Boris Johnson and Michael Gove have relentlessly campaigned on the theme of immigration.

The leave campaign appears to have picked up three percentage points. The potential in the leave campaign’s strategy is reflected in responses suggesting that two in five voters (41%) cite immigration as one of their two most important issues when deciding how to vote. Just over a third (35%) cite Britain’s ability to make its own laws without EU interference and 29% cite the impact of leaving on the UK economy.

Half of the 2,007 people surveyed said they believed immigration would be under better control if the UK did leave the EU. Twelve percent felt the UK would have more control if the country retained its EU membership, and 24% said there would be little difference.

Johnson is expected to launch a campaign to highlight the security dangers of EU membership, including the possibility of Turkey’s accession to the EU, this weekend.

However, the leave campaign also believes that, if it can keep the headline polls close, a relatively poor turnout among Labour voters who support remain could deliver it victory.The findings came as Johnson, who has been posing increasingly as a prime minister in waiting, told the Observer that he believed no genuine “liberal internationalist” could support the EU.

The former mayor of London joined forces with Gove, the justice secretary, to suggest that a vote for Brexit could deliver improved social justice. He added: “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. 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 poll by Opinium also issued a different set of figures using an alternative methodology to try to reflect the fact that online samples are sometimes seen to over-represent socially conservative respondents, who may be more likely to favour Brexit.

With the adjustments to the make-up of the sample surveyed, remain keeps its lead. Opinium found that 43% of UK adults said they would vote to remain in the EU in a referendum, while 41% would vote to leave the EU and 14% don’t know how they would vote.

However, Opinium said a move to leave had also been reflected in answers to their so-called “nudge” question, which asks those who do not yet know how they will vote in what direction they are leaning. In the last Opinium survey two weeks ago, those split 55% leaning to remain and 32% leaning towards leave.

In the latest survey, the gap has narrowed dramatically, with 36% leaning towards remain and 33% towards leave, even when the methodological updates were implemented. When those who did not know were forced to choose, 47% said they leaned more towards remain, while 32% leaned more towards leave.

Generally the polls show an electorate split by social class, region and party political affiliation. The more affluent favour staying in the EU, while older people are typically more likely to back Brexit.

London is a stronghold of the remain camp, while the East Midlands tends toward leaving. Areas such as north-west England are more evenly poised.

Nearly half (48%) say Cameron should resign if Brexit occurs, 32% that he should not. Remain voters are evenly split (42% either way) while leave voters overwhelmingly say he should resign (65% to 22%).