Britain cannot carry on as it was before Brexit and must cut taxes and reduce regulation, Lord Frost said on Monday as he called for "free debate" over government policy.
In a speech at a conference attended by Boris Johnson, the Brexit minister urged the UK not to import the "European social model" or it would risk the failure of its split from the EU.
His intervention came amid growing reports of concern about drift in Number 10, compounded by a chaotic speech given by Mr Johnson to the Confederation of British Industry (CBI) on Monday.
Laura Kuenssberg, the BBC’s political editor, quoted a senior Downing Street source as saying senior Tories needed to "wake up" and call for changes.
"There is a lot of concern inside the building about the PM … it’s just not working," the source reportedly said. "Cabinet needs to wake up and demand serious changes, otherwise it’ll keep getting worse.
"If they don’t insist, he just won’t do anything about it."
On Monday night, the Prime Minister was facing a rebellion in the Commons over social care reforms after ministers made changes that critics believe "disadvantage the less well-off".
Although the rebels were set to fail, the backlash is set to spread to the Lords, where former ministers will attempt to force a climbdown.
In an intervention that will be seen as reflecting wider Tory concerns over tax rises, Lord Frost said on Monday: "I can’t share the views of those who think we can treat the private sector as just a convenient way of keeping the public sector running.
"It isn’t just a source of taxes. Nor is it a bunch of people who will inevitably do bad things unless the Government keeps a very close eye on them. We can’t carry on as we were before and if, after Brexit, all we do is import the European social model, we will not succeed."
There has been widespread disquiet among Tory MPs in recent weeks as the botched handling of the Owen Paterson lobbying row saw Labour pull ahead in opinion polls.
Cabinet ministers are being sent to campaign in Old Bexley and Sidcup ahead of next week’s by-election – a sign of the precaution being taken over what should be an easy hold for the Tories.
Under Mr Johnson, the tax burden has risen to its highest level in 70 years despite both the Prime Minister and Rishi Sunak, the Chancellor, insisting that they are low-tax Tories at heart.
Speaking at the Centre for Policy Studies conference, Lord Frost said: "The formula for success as a country is well known. Low taxes – I agree with the Chancellor, as he said in his Budget speech, our goal must be to reduce taxes – light-touch and proportionate regulation, whatever our policy objectives."
Calling for debate on government decisions, Lord Frost, one of three ministers who spoke out in Cabinet against the National Insurance rise earlier this year, said: "To make the best decisions, we need the fullest and freest possible debate.
"I believe that free debate is a good thing. It forces everyone to test their arguments, and I strongly believe it means the best ideas win."
UK tax take highest in 70 years – Burden of tax as a % of GDP
Earlier on Monday, Mr Johnson made a speech outlining his pro-business vision to the CBI – but the message was overshadowed by perceived blunders in his delivery. In the address, he invoked Peppa Pig as proof of the power of the free market and jokingly likened himself to Moses as he argued the case for a green revolution.
On social care, Dan Poulter, a former health minister, and Mark Harper, a former chief whip, were among the Tory MPs set to rebel against an amendment to the Health and Care Bill that will see it take longer for those assisted by the state to hit the £86,000 cap on costs.
Mr Harper said: "It potentially disadvantages the less well-off and those of working age with life-long conditions. I will be voting against it."
Tens of Tory MPs are said to be minded to rebel or abstain in the vote. One Tory said there was "a lot of discontent", while another predicted: "This has got legs. It is picking up a head of steam. It will run – the Lords will do lots of things."
Amid a fierce whipping operation, some planned to abstain rather than rebel in the expectation that the Lords would send the legislation back to the Commons for reconsideration.
Lord Lansley, a former Conservative health secretary, and Baroness Altmann, an ex-pensions minister, told The Telegraph they would seek to amend the legislation when it arrived in the upper chamber.
On Monday night, Mr Johnson’s allies in government brushed off criticisms of him, arguing that they were politically motivated. But one adviser to a Cabinet minister told The Telegraph: "There is just a lot of stress. The PM’s obviously very, very unhappy. No PM wants to be in a rough patch. It is not out of the ordinary. I would imagine he’s not enjoying it."
Sir Keir Starmer, the Labour leader, piled further pressure on Mr Johnson by touting his plans to abolish business rates and doubling down on opposition to the Government’s National Insurance rise.
He told the CBI: "The reason we opposed the Government’s tax rises now is because business said to us that ‘as we come out of the pandemic and we are trying to get back on our feet, the last thing we need now is to be held back by tax’."