The Leave campaign has been handed a significant boost after slashing Remain's 13-point lead from a week ago, to just five currently, according to an ORB poll. The latest reading comes after figures showed that annual net migration to Britain rose to 330,000 in 2015, suggesting the Leave campaign's focus on a lack of control over immigration has helped its case with just over three weeks to go before the EU referendum.

The most recent poll – in which 800 people were surveyed – puts Remain on 51%, with Leave trailing on 46%. Some 52% of respondents believed that a Brexit would improve the immigration system (up 2%), compared to 23% of those who wish to stay in the EU (down six points).

Meanwhile, Remain appears to have gained ground on terrorism. According to the findings, both sides are deadlocked on the issue, with 35% of voters from each camp saying a vote to the contrary would expose the UK to a greater risk of terrorism. In the previous reading on 24 May, Leave had a nine-point advantage over Remain (39% to 30%.)

Sir Lynton Crosby, the political strategist behind the Conservative election victory, said caution must be exercised over the latest findings after last week's poll "may have been overly positive for the Remain camp." He also warned the Leave camp about complacency, saying voters "are not yet locked in" and noted the increase in the number of Brexiteers who are likely to change their mind – up two points to 14%.

Analysing the data in the Telegraph, Crosby wrote: "Despite the drop-off in the Remain campaign's support, they do still lead on both vote and the metrics about campaign performance detailed above and thus hold a strong position with less than four weeks to go."

He added: "The reality is that at this stage, the Leave and Remain campaigns have two different strategic imperatives. The challenge for the Remain campaign is to identify and motivate their voters to actually show up on 23 June.

"Twice as many voters in this poll cite Leave as a risk as think remaining in the UK is a risk. This could continue to be the best way to motivate Remain voters to turn up. The challenge for the Leave campaign is to persuade more voters of their position."

Meanwhile, more than 200 Cambridge University academics expressed "grave concern for the future of our universities and country if Britain votes to leave the EU." Writing a letter in their personal capacities, professors, dames, knights and Nobel Prize winners warned that a Brexit would lead to a funding black hole that the government would be unable to fill.

"British universities are among the most successful centres of learning and research in the world," reads the letter signed by the likes of the former Archbishop of Canterbury, Lord Rowan Williams, and the historian, Sir Richard Evans.

"They are significantly helped in this by funding from the EU. In the sciences, we have 22% of European Research Council grant-holders, with only 12% of the EU's total population," the letter from the academics continues. "In the arts and humanities, around 30% of major interdisciplinary projects at Cambridge would be at risk without EU backing. The Government would not be able to replace this scale of funding if we voted to leave."

The academics also said that the rise of academic centres in America and Asia mean Britain's leading position in research and innovation can only continue within a reformed EU. In a stark warning, senior figures from the elite educational institution said: "Our future economic growth depends on it."