A focus on health came ahead of spending on law and order (23 per cent), education (20 per cent), the environment (ten per cent) and defence (two per cent).
Support for the NHS was also evident from the YouGov poll; 93 per cent said they regard it as an essential free public service.
Record increases in NHS funding are expected to be reduced later this year as part of the government's spending review.
But Dr Peter Carter, general secretary of the RCN, said that support for the government will weaken if it fails to support the NHS.
"This survey is proof that the public value and believe in our NHS; that they want modernisation, not privatisation; and that they demand increased investment in order to maintain the welcome progress made in recent years," he added.
"The NHS is a unique public institution with a unique role in our national life and it should be supported and sustained. That's what the public believe and that's the message our politicians need to hear and act upon".
A spokesperson for the Department of Health (DoH) said that the government would continue to place an emphasis on funding the NHS.
"The NHS budget has doubled since 1997 and will have almost tripled by 2008. This extra money has cut waiting times, built new hospitals and surgeries, paid for more doctors and nurses to work and train, and improved access to healthcare for millions of people. Even more will be going in next year - about £6 billion extra, an increase of over nine per cent from this year," the spokesperson said.
"All parts of the NHS are consistently delivering for patients against national priorities - even amid financial pressures in a minority of organisations. NHS organisations continue to use their record increases in funding to speed up treatment and improve quality of care for patients."
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