Daily Mail readers are increasingly pessimistic about the state of Brexit negotiations, with only a quarter of them believing it is likely that Britain will get a good deal with the EU and 86% of them agreeing that the process of leaving the EU “has been a mess”.

Despite this, they are still overwhelmingly in favour of exiting the EU, with two-thirds saying they would vote to leave if the vote was re-run tomorrow, according to a major new poll examining the attitudes of newspaper and website readers towards Brexit.

The research, conducted by the independent polling firm YouGov on behalf of the People’s Vote campaign for a referendum on the final Brexit deal and shared with the Guardian, found that readers of many publications are substantially more pro-remain than the editorial line of their favoured newspaper would suggest.

Almost half of all Daily Telegraph readers would vote to remain if they were given a second chance, while 60% of readers of the Sunday Times – which backed Brexit in 2016 – would support staying in the EU. A majority of people who read Metro, which recently overtook the Sun to become Britain’s biggest print newspaper, would also back remain.

The Daily Mail’s print edition, seen as important political indicator for Theresa May’s government, is now being edited by Geordie Greig, a former remainer who has signalled his intention to support a soft Brexit. Crucially for the prime minister and Conservative politicians, the poll found Mail readers believe that if the UK gets a bad Brexit deal, it will mainly be the fault of the UK government, rather than EU officials.

Even among Brexit supporters, the poll found deep suspicion of the government’s ability to deliver on promises made during the EU referendum. More than 70% of Sun readers agreed “it is likely that many of the promises made by politicians in favour of leaving the EU will be broken”.

The polling was produced through an unusually large representative survey of more than 25,000 people. Although it is increasingly hard to define a publication’s readership in an era where media consumption has splintered, YouGov considered people who had read the print newspaper in the last year or visited a website in the last month.

The Guardian’s readership was among the most strongly pro-EU, with 84% of print readers and 79% of online readers saying they would vote remain if a referendum were held again today. Two-thirds of Guardian readers said they believed the NHS would get worse if Britain left the EU, compared with just a quarter of Daily Express readers.

The poll found slightly softer support for a referendum on Britain’s final deal with the EU, with a narrow majority in favour among the general public among those who expressed a firm view either way.

Readers of newspapers’ websites were generally more supportive of the EU, possibly reflecting their generally younger readerships. The polling found that the majority of users of the pro-Brexit Telegraph website would support remain in a second referendum. Meanwhile, readers of MailOnline and the Sun’s website would only narrowly vote for Brexit, despite the full-throated backing of their parent papers for leaving the EU.

Consumers of the print edition of the relentlessly pro-Brexit Daily Express were the most upbeat about the chances of Britain striking a good deal.