Polling by Ipsos Mori found that 61% of people in Britain consider the NHS to be among the biggest issues facing the country, up 13% from last month.
The finding suggests public concern about the NHS is at its highest level since then-chancellor Gordon Brown announced a £40bn NHS investment plan in 2002.
Brexit and Europe remains the top issue people point to if asked to pick out a single most important issue facing Britain, with 32% choosing it as the number one issue. The NHS ranks second, on 21%.
However, asked to pick out multiple issues that are among the biggest facing Britain, more people highlight the NHS in their choices than any other issue, with 61% picking it out. This compares with just 45% for Brexit, in second place, 27% for education/schools and 25% for immigration.
King's Fund policy fellow Dan Wellings, writing in a blog on the think tank's website today, warned: 'The Ipsos MORI/Economist May 2017 Issues Index found that 61% of people identify the NHS as one of the most important issues facing the country, 16 percentage points above Brexit. This is the fifth highest level of concern recorded since 1997 and the highest it has been since April 2002.
'The warnings around inadequate NHS funding have been growing in number and volume over the past few years and now seem to be cutting through with the public in a significant way.
'Despite this, in a Brexit-dominated campaign and with sharply polarised views about the strengths and weaknesses of the main parties, most commentators do not think the NHS will be a decisive factor at the ballot box. However, such high levels of public concern do suggest that the NHS will need to be a high priority for the incoming government.'
In a strongly-worded speech at last month's LMC conference 2017, GPC chair Dr Chaand Nagpaul urged GPs to ask their patients to vote for a government that would fund the NHS properly.