More than a quarter of Brexit voters feel that they were misled by the Vote Leave campaign and its chief cheerleader Boris Johnson, a new Opinium poll has found. The online survey, of more than 2,000 people between 15 and 18 August, revealed that 26% of Leave-backing respondents said they felt that way a year after the Brexit vote on 23 June 2016.

Vote Leave, backed by Johnson, Michael Gove and former Labour MP Gisela Stuart, said that £350m per week could be spent on the NHS if the UK quit the EU. The contentious figure was challenged by the UK Statistics Authority, which stressed that the UK paid its budget contribution to the EU after receiving its rebate.

But Dominic Cummings, the former Gove aide who played a central part in the Vote Leave campaign, has maintained that the figure was accurate, pointing out that the UK's gross contribution to Brussels worked out to be £367m per week in 2014.

In a letter to Cummings, Sir Andrew Dilnot, the chair of the UK's Statistics Authority, said: "The UK's official gross contribution for 2014 before the application of the rebate was £19.1bn. As I have made clear previously, this is not an amount of money that the UK pays to the EU each year. The full £19.1bn is not a net contribution."

Elsewhere, Vote Leave also endorsed an Australian-style via system, a points-based scheme that Theresa May ruled out following the Brexit vote.

The study comes during the two-year-long talks between the UK and the EU. The British government has indicated that it wants to split from Brussels' customs union and single-market, while the EU wants Brexit Secretary David Davis to commit to a so-called 'divorce bill'. The move could cost the UK up to £91bn.

On the issue of who the British public trust most to lead the Brexit negotiations, the Opinium poll discovered that 38% of respondents trusted the Conservatives, 19% Labour, 6% Ukip and 4% the Liberal Democrats.

James McGrory, executive director of Open Britain, said: "Vote Leave ran a campaign of deliberate falsehoods, and this poll proves that even many of their own voters have woken up to that fact.

"Virtually all their big promises have been shown to be worthless. There will not be an extra £350m a week for the NHS. Voting for Brexit has made families worse off. A hard Brexit will mean less money for public services, not more.

"Cabinet ministers involved in Vote Leave, like Boris Johnson and Michael Gove, should apologise for their actions during the referendum and end their support for a destructive hard Brexit."