Cameron criticises comedian but says he has not had time to look at allegations about singer Gary Barlow's tax affairs

David Cameron has criticised the comedian Jimmy Carr, describing him as "morally wrong" for seeking to avoid taxes.

Media reports of Carr's financial arrangements suggest "straightforward tax avoidance", said the prime minister, and it was unfair on the people who pay to watch him perform that he is not paying his taxes in the same way that they do.

Cameron said he had not had time to look at allegations relating to singer Gary Barlow, who was given an OBE in the Queen's birthday honours list.

Speaking to ITV in a round of TV interviews during his trip to Mexico, the prime minister said: "I think some of these schemes – and I think particularly of the Jimmy Carr scheme – I have had time to read about and I just think this is completely wrong.

"People work hard, they pay their taxes, they save up to go to one of his shows. They buy the tickets. He is taking the money from those tickets and he, as far as I can see, is putting all of that into some very dodgy tax avoiding schemes.

"That is wrong. There is nothing wrong with people planning their tax affairs to invest in their pension and plan for their retirement – that sort of tax management is fine. But some of these schemes we have seen are quite frankly morally wrong.

"The government is acting by looking at a general anti-avoidance law but we do need to make progress on this. It is not fair on hardworking people who do the right thing and pay their taxes to see these sorts of scams taking place."

Carr, who has lampooned bankers for failing to pay their tax, reportedly protects £3.3m a year by channelling cash through Jersey-based company K2, which then returns the money in the form of a loan. This is not subject to income tax.

The comedian defended his financial affairs on Tuesday, telling an audience: "I pay what I have to and not a penny more."

The Channel 4 standup is reported to have used a legal tax-avoidance scheme that enables members to pay income tax rates as low as 1%.

He spoke out amid claims that members of Take That – Gary Barlow, Howard Donald, Mark Owen and the band's manager, Jonathan Wild – invested at least £26m in another scheme run by Icebreaker Management Services.

Earlier, a Downing Street spokeswoman had said Cameron backed George Osborne's description of aggressive tax avoidance as "morally repugnant".

Asked if Cameron was "disappointed" about the reports of the tax affairs of Barlow, who was made an OBE in the Queen's birthday honours at the weekend and campaigned alongside the Tory leader at the general election, she said: "I just go back to the general point about tax, that everybody should pay the right level of tax.

"Separately, the jubilee celebrations were a great success and Gary Barlow played a big part in that."

Asked if the government might consider whether the tax affairs of individuals should be a factor when considering people for honours, she said: "I am not going to comment on individuals in terms of what's happening in a newspaper report."

Later, another Downing street source appeared to harden the government's position on celebrities' tax affairs, and said: "All tax avoidance schemes need to be addressed by HMRC [HM Revenue & Customs] whichever big-name stars are involved."

Separately, No 10 sources stressed that a general tax avoidance rule, due to come in next year is the best way of handling these kind of tax loopholes, rather than constantly chasing down every individual tax scheme.

Carr was confronted over his financial arrangements during a show in Tunbridge Wells, in Kent.

Challenged by a member of the audience, who told him: "You don't pay tax", he replied: "I pay what I have to and not a penny more,", the Times reported.

It came after he appeared to make light of the furore surrounding his tax payments.

He asked: "Got through the papers? I haven't really been through the papers today. The Murdochs are after me …"

Carr is said to be one of more than 1,000 beneficiaries who shelter £168m from the taxman each year using K2.

Barlow, Donald, Owen and Wild are among almost 1,000 people who contributed £480m to 62 partnerships in music industry investment schemes, the Times reported.

An HMRC spokesman said it had successfully challenged an avoidance scheme run by Icebreaker LLP, winning on the main arguments in the tribunals.

The spokesman said: "We are now preparing to litigate Icebreaker 2 but for legal reasons cannot say more at this time. We examine the implementation of avoidance schemes in detail and will not let any aspect of these cases go unchallenged."

HMRC said the K2 scheme was already under investigation.

The spokesman added: "We have taken firm action to protect the exchequer from unacceptable tax loss.

"We do not accept that the Icebreaker tax avoidance schemes have the tax effects their promoters claim – we have already successfully challenged one Icebreaker scheme in the tribunal."

HMRC could not confirm whether or not members of Take That and their manager had been involved in an Icebreaker 2 scheme.

Writing in the Sun, the Treasury chief secretary, Danny Alexander, warned stars and others who employ "ever more obscure and underhand" avoidance measures

"No matter how rich or famous you are, we are coming to get you," he wrote.

"When it comes to paying their fair share, some of the people who can afford it most think they can get away with paying the least.

"Frankly, I think people who dodge the tax system are the moral equivalent of benefit cheats. Both sets of people think they can bend the rules everyone else lives by for their own benefit," he wrote.

A spokesman for Icebreaker Management Services Limited said the LLPs [limited liability partnerships] were commercial businesses, in which the LLP members worked actively together in order to produce creative and artistic material and generate taxable profits.

"As a result, hundreds of people have been, and can continue to be, employed in the creative industries and large numbers of products have been made for distribution and sale around the world.

"We believe that the Icebreaker LLPs play a valuable part in the UK economy, frequently fostering and supporting creative talent and young people embarking on their careers.

Icebreaker Management Services Limited recognises the need for the proper administration and collection of taxes but that its partnerships were legitimate commercial enterprises which generate taxable profits., and that it is essential that anyone who seeks to make use of tax relief does so properly and within the law.

"Abuse of the tax system for personal gain is, of course, never acceptable," the spokesman said.

Catherine McKinnell MP, the shadow exchequer secretary to the Treasury, said: "Tax avoidance must be clamped down on, especially at a time when families, pensioners and businesses who pay their fair share are feeling the brunt of the double-dip recession.

"But this week's revelations show that, for all their tough talk, the government is failing to tackle the problem. Cutting the resources of HMRC too far and too fast will make it even harder for the government to stay ahead of clever accountants.

"And at the same time as they are failing to tackle tax avoidance. David Cameron and George Osborne are actually cutting taxes for millionaires while asking millions of families and pensioners to pay more."

Fresh tax questions emerge

Tax questions have also dogged a number of Tory donors and advisers:

1 A mobile phone company that has paid no corporation tax for three years has become the Conservatives' most generous corporate donor after giving more than £300,000 over the last nine months.

Lycamobile, an £88m company based in Canary Wharf, gave more than £130,000 between January and March this year, the latest Electoral Commission records show. The company says it has paid all tax owing and has re-invested its profits.

2 Lord Ashcroft, the Tories' former treasurer who has given more than £10m to the party, revealed in 2010 that he was "non-domiciled", meaning he did not pay UK tax on earnings made outside Britain. When he was made a peer in 2001, at the behest of the then Tory leader William Hague, he gave assurances that he would take up permanent residence in the UK. Ashcroft insists that he has behaved properly and has paid all taxes due.

3 Sir Philip Green, the Topshop billionaire who was appointed as a government adviser in 2010, has been accused of avoiding a personal tax bill of £300m. Green's family banked one of the biggest pay cheques in corporate history in 2005 when his Arcadia fashion business, which owns Topshop, paid a £1.2bn dividend. The record-breaking payment was made to his wife, Tina, who lives in Monaco and is the direct owner of Arcadia. As a result, no UK income tax was due. He says criticism of this is outrageous and says he has paid "tens of millions" in tax to Britain.

4 An unnamed Tory donor avoided tax by flying outside UK airspace on his private jet at night, a lobbyist claimed in April. The millionaire is said to have routinely flown out of Luton airport in the evening so he could sleep on his jet.

Because he was outside British jurisdiction at night, this allowed him to extend the number of days he could stay in the UK without paying tax. As a non-resident, he could spend just 91 full days in the country each year. The arrangement was revealed to undercover reporters by Sarah Southern, the lobbyist at the centre of the recent cash-for-Cameron scandal.