More people will become ill as a direct result of the government cutting spending on public health, which will put the NHS under further strain, a parliamentary report on Wednesday warns.

Peers on a House of Lords select committee urged citizens to do more to demonstrate personal responsibility – their “common duty” – to live healthily in order to help preserve the NHS as a tax-funded system that is free at the point of use.

They blame “the short-sightedness of successive governments” for leaving the NHS underfunded, understaffed and woefully unprepared for the huge pressures now bearing down on it.

In a strongly worded report, the House of Lords select committee on the long-term sustainability of the NHS claims that cuts of £531m to public health budgets in England during this parliament could backfire badly. “Continued cuts to the public health budget are not only shortsighted but counterproductive. There is a grave risk that the burden of disease will increase if these cuts continue, a trend which is bound to result in a greater strain on all services,” it says.

Evidence submitted to the inquiry showed that the public health budget for England was cut by £200m in 2015-16 and will shrink by a further £331m by 2021. Services to help people stop smoking and manage their weight are also at risk, the report says. Peers were “totally unconvinced” by the health secretary Jeremy Hunt’s insistence that reducing the budget would not necessarily impede progress on public health.

The committee, which includes both Labour and Conservative former health ministers, recommends ministers launch a nationwide campaign to highlight the risks to health of being overweight.

A failure to stem the rising tide of dangerous obesity risks even more people having a heart attack or stroke or developing cancer or diabetes, “under which the NHS will surely buckle if radical action is not taken”, warned the Royal Society for Public Health.

But it cautioned that socioeconomic factors can make it difficult for poorer people to live healthily. “If we are to expect the public to make healthier lifestyle choices, we must also empower them to do so. We still live in a country where social and environmental factors predetermine many of our health outcomes and where the ‘choice’ to live healthily or unhealthily is illusory for many,” said Shirley Cramer, the RSPH’s chief executive.

The peers say: “The government should be clear with the public that access to the NHS involves patient responsibilities as well as patient rights. The NHS constitution should be redrafted with a greater emphasis on those often overlooked individual responsibilities.”

An overhaul of the constitution is needed “as part of a renewed and sustained drive to improve health literacy and educate the public about their common duty to support the sustainability of the health service”, they add.

The committee also warns that a lack of proper workforce planning to meet predicted rising demand for care means that understaffing is now “the biggest internal threat to the sustainability of the NHS”. Prolonged pay restraint in the service has also contributed to poor morale and staff quitting, peers have found.

Hunt rejected the committee’s claims that it has done too little. “This government has a strong track record on public health. Cancer survival is at a record high, whilst smoking and teenage pregnancies are at an all-time low,” a health department spokesman said.

“Over the course of this parliament we will invest more than £16bn in local government public health services, but we have also shown we are willing to take tough action to protect the public’s health – introducing standardised packaging of cigarettes and a soft drinks industry levy, and launching a world-leading childhood obesity plan.”