It has been estimated that the health service would receive an estimated £2.75 billion more in funding each year if everyone paid the extra £1 a week. The poll also indicated that just over half of people would be prepared to pay an extra £2, which would reportedly raise an estimated £5.5 billion. But what do you think? Vote in our own reader poll below.
Meanwhile, just under a third of people would pay an extra £5 a week, raising £13.75 billion a year for the NHS, the research suggested.
Two thirds of people who took part in the survey said they would be prepared to see income tax rates rise by 1% if the money went to the NHS.
A 2015 study by the Institute for Fiscal Studies estimated the extra 1% on all rates of income tax would also raise £5.5 billion.
Shadow Health Secretary Jonathan Ashworth said the poll confirmed the British public "just don't trust the Tories with the NHS".
Speaking to the Daily Mirror, which reported the research, he said: "Eight years of underfunding has left services overstretched and patients at risk.
"Around the country brilliant NHS staff are going the extra mile to keep the service running but are being let down by this Government."
Health Secretary Jeremy Hunt recently told the Commons Health Committee that he did not think "any health secretary is ever going to not support potential extra resources for his or her department".
There was also a call for more funding for the NHS from within Theresa May's Cabinet in a notable intervention from the Foreign Secretary.
Boris Johnson was reported to be pressing for an extra £5 billion for the NHS, including money from any "Brexit dividend".
However, Chancellor Philip Hammond said he had given Mr Hunt an extra £6 billion at the recent Budget.
"We will look at departmental allocations again at the spending review when that takes place," he said.
The Mirror's online survey by Survation, which polled more than 1,050 adults, found that 27% would not be prepared to see the 1% rise in tax.
The poll asked respondents: "Some people say there is a 'winter crisis' in the NHS and that it is underfunded. With this in mind, which of the following do you think is the best way to fund the NHS?"
Exactly half said taxation was the best way to raise money for the health service, while 17% said services should be charged for.
Around the same number said a type of insurance model would be best, while 18% said they did not know what would be the best option.