Voters are ready by nearly two to one to pay more tax to bolster the NHS. A large face-to-face survey carried out before the winter crisis struck the health service in November has recorded the biggest-ever shift of opinion on the issue.

The poll, carried out by the respected British Social Attitudes research centre, has recorded a jump from 41% support for higher taxes in 2014 to 61% at the end of last year. An even higher proportion, nearly nine in 10 people, thought there was a funding crisis.

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It also found a matching rise in opinions about the quality of NHS care, with nearly three times as many saying healthcare was declining, with most expecting it to get worse still. Only a fifth thought the standard of care would improve.

Theresa May has promised higher funding for the health service, but not until after a spending review this autumn. At current estimates, the NHS in England alone will be £900m in deficit by the end of this year, and Jeremy Hunt, the health and social care secretary, is calling for a 10-year pay settlement as part of a push for a significant increase in spending.

Concern about the NHS ranks with Brexit as one of the two biggest worries for voters. There is widespread consensus that more money must be found, and there has been a growing debate about the best way of doing it – with opinion divided between raising income tax, raising national insurance (as Gordon Brown did to bring NHS spending to the EU average in 2002) or bringing in a dedicated NHS tax.

The poll comes as the latest figures for waits in NHS accident and emergency showed another fall in the numbers treated within the four-hour target time, with the number of patients waiting more than a year for treatment over 2000 for the first time in more than five years, and the 18-week target for planned treatment missed for the second year in a row.

An unprecedented cross-party alliance of senior MPs, including the chair of the health committee, Dr Sarah Wollaston, has asked for NHS funding to be taken out of party politics altogether.

In an unusual move, the appeal, which was launched at the end of March, was backed by Sir Nick Macpherson, the former permanent secretary at the Treasury, who supports a hypothecated NHS tax.

The Treasury has always been opposed to any tax that it does not control, and it remains formally opposed to the hypothecation proposed by its former top official. There are also concerns that although a hypothecated tax would be transparent for taxpayers, if the tax base shrank in an economic downturn, it might not raise enough to pay for health services.

The 2p increase in national insurance that Brown levied in 2002 to bolster spending was soon outstripped by the growth in demand and technological improvements. But a clear link between what is raised and how it is spent is becoming increasingly desirable as politicians seek new ways of gaining voters’ trust.

The survey, sponsored by the health thinktank the King’s Fund as part of its tracking of public attitudes to the NHS, also found that more than half of Conservative voters who took part backed a tax rise to pay for the health service, up from 33% in 2014; support among Labour party voters stood at 68% in 2017.