Opinium/Observer poll shows 48% of Tory voters want to stay, up from 39%, while remain now has a four-point overall lead

David Cameron’s campaign to keep the UK in the EU appears to be working as Conservative voters switch to the remain camp, the latest Opinium/Observer referendum poll suggests.

With a month to go before voters decide whether Britain should stay in or leave the EU, Opinium puts remain four points ahead on 44%, with leave on 40% and 14% undecided. At the beginning of April, leave had a four-point lead.

Remain now has a substantial lead among Conservative voters with 48% of Tory backers saying they want to stay in the EU, compared with 41% who want to leave.

This is a considerable turnaround since the first Opinium/Observer referendum poll in early April, which showed 44% of Conservative voters in favour of leaving against 39% who backed staying in.

Adam Drummond, of Opinium Research, which carried out an online poll of 2,008 adults between 17 and 19 May, said: “There does seem to have been some move towards staying in the EU, particularly given that ours is an online methodology which typically shows a closer race than polls conducted on the phone. The change comes mainly from Conservative voters who have moved from narrowly backing Brexit at the end of April to a large lead for remain.”

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Drummond said the change appeared to be significant though it could in part be the result of hardline pro-Brexit Tories now identifying themselves as Ukip supporters. This would mean that the proportion of pro-Brexit Tories would drop in the figures.

When asked how important the referendum was, more than half (54%) said they believed it was more important than a general election while 39% thought it was about the same level of importance.

Two-thirds (67%) of those planning to vote leave thought it was more important than a general election against 47% of those planning to vote to remain.

Three-fifths of respondents (61%) said they had discussed the referendum with family members and 54% had done so with friends. Ukip supporters discussed the referendum most, with 76% of party supporters saying they had raised it with family and 70% with friends.

While the lead for remain is still narrow, more than twice as many respondents said they expected the UK to remain in the EU (52%) as those who thought it would vote to leave (23%). Of remain supporters, 76% think their side will win while only 46% of leave’s backers are expecting success.

Opinium also asked what effect people thought Brexit would have on their financial security, with 31% saying they thought their household would be less financially secure if Britain voted to leave, while 17% believed it would be more secure.

Almost nine in 10 (87%) of respondents say they are definitely registered to vote, while a further 6% think they are. However, only 70% of 18 to 34-year-olds say they are definitely registered to vote compared with 97% of those aged 55 and over.

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• Opinium Research carried out an online survey of 2,008 UK adults aged 18+ from 17 to 19 May 2016. Results have been weighted to nationally representative criteria.