Britain's "health and safety culture" will be killed off for good by the government, David Cameron declared as he warned that a "monster" was hampering business growth. In his first public appearance of 2012, intended to show that boosting economic growth is the government's main priority, he also said local authorities needed a "slap" to encourage them to work more effectively with businesses.

But Cameron admitted the government had made a mistake in one of its first initiatives to boost economic growth. A national insurance holiday, introduced for new businesses outside London and the south-east in September 2010, had created fewer jobs than expected, he said. "It wasn't as successful as we hoped," he said at the headquarters of Intuit, a financial software and services firm, in Maidenhead. "It was perhaps too complicated, it was too targeted at specific businesses in specific areas of the country and so it didn't work as well as we hoped."

However he last night vowed not to give in to pressure to scale back austerity measures. He said it would be "the wrong thing to do" after a poll by ComRes for ITV News showed 59% of voters wanted a slowdown in spending cuts if economic forecasts remain grim. The survey by ComRes for ITV News, conducted in November and December, suggested just less than a quarter of the public (24%) backed a continued hardline stance irrespective of the conditions.

Cameron told ITV News he was determined not to alter course – even if it meant being defeated at the next general election. "I would rather be a one-term prime minister who does the right thing than a two-term prime minister who does the wrong thing," he said.

His main message of the day was the announcement of new relief for businesses complaining of excessive health and safety regulations. In an article for the London Evening Standard, he wrote: "One of the coalition's new year resolutions is this: kill off the health and safety culture for good. I want 2012 to go down in history not just as Olympics year or diamond jubilee year, but the year we banished a lot of this pointless time-wasting from the economy and British life once and for all."

Cameron announced that lawyers will face a cap on their earnings in cases for claims of up to £25,000. Businesses have complained that they settle cases in which an aggrieved employee has a weak complaint in order to avoid paying legal fees.

"I think that will take a lot of fear out of the health and safety monster and make sure that businesses feel they can get on, they can plan, they can invest, they can grow without feeling they are going to be strangled by red tape and health and safety regulation."

He said the law would change to ensure that businesses are no longer considered automatically to be at fault if something goes wrong. The demands of insurance companies will also be investigated. "Of course it is in their interests to guard against reckless practices, but there is a risk that the dial can swing from sensible to insane levels of compliance, forcing businesses to go far beyond what is required by the letter of the law."

Speaking at the headquarters of Intuit in Maidenhead, he said: "I don't think there is any one single way you can cut back the health and safety monster," Cameron added. "You have got to look at the quantity of rules, and we are cutting them back. You have got to look at the way they are enforced, and we are making sure that is more reasonable."

Richard Jones, head of policy at the Institution of Occupational Safety and Health and Public Affairs, said: "Labelling workplace health and safety as a monster is appalling and unhelpful, as the reason our legislative system exists is to prevent death, injury or illness at work, protecting livelihoods in the process. The problem identified by the government's own reviews is not the law, but a rather exaggerated fear of being sued, fed by aggressive marketing."

Cameron also said the government would look at granting loans to young entrepreneurs at a similar rate to those provided to university students. "I think it is a brilliant idea," he said in response to a question from a Virgin Media Pioneer, Zoe Jackson, about a Richard Branson proposal to set up a youth investment fund. "We are providing loans for students to go to university. Why not look at something similar for people who have a great business idea and want to get started?"

The prime minister said he wanted to highlight business because the British economy faced a tough year. Ministers have been managing expectations for the economy downwards amid fears the eurozone crisis could spark a double-dip recession.

"This is going to be an absolutely vital year for the British economy and also a difficult year for the British economy," he said.

"We have seen a squeeze on household budgets as food and fuel prices have risen. We have got the difficulties in the eurozone that have cast a bit of a freeze across Europe's economy.

"So it is going to be a tough year. But it is not a year in which the government is going to stand back … it is a year in which the government is going to roll up its sleeves and ask what can we do to help business."

Cameron also said he wanted local authorities and businesses to work more closely together, adding: "It sounds like they need a slap rather than a nudge. In a good local authority, there should be a small business adviser who is there to try and help make sure that local authority is business-friendly."

The government will offer incentives to local authorities by allowing them to keep more of the rates from new businesses in their area, he said, adding: "At the moment, there isn't really an incentive for local government to be friendly to local business."

While Cameron was keen to show that the government would make economic growth its main priority, the poor performance of the national insurance holiday had shown Whitehall schemes can only have a limited success.

"You can come up with all the schemes in the world," he said. "But actually there is no scheme that is as good as controlling your spending, getting the debts under control and therefore keeping your taxes down – and particularly keeping the taxes down that cost businesses when they employ people."

Owen Smith, Labour's shadow exchequer secretary to the Treasury, said: "Now that the prime minister has admitted the scheme has failed – and more importantly why it failed – the government should heed Labour's calls for the tax break to be extended to all small firms that take on extra staff in every part of the country. This move, which is part of Labour's five point plan for jobs, would benefit thousands of small businesses across the whole of the UK and help to create desperately needed jobs. Getting businesses growing and people into work is vital if we're to successfully get the deficit down."

The prime minister will focus on Friday on the work of nurses as he speaks of how he was "absolutely appalled" by a finding by the Care Quality Commission that one in five hospitals are failing to feed patients properly. The government will make nurses focus on "patients not paperwork" by ensuring they carry out regular rounds and that a figure of authority is present on every ward.

"We are going to get rid of a whole load of bureaucracy that stops nurses from doing what they do best. And in return patients should expect nurses to undertake regular nursing rounds – systematically and routinely checking that each of their patients is comfortable, properly fed and hydrated, and treated with the dignity and respect they deserve," he will say.