PM's spokesman says Gordon Brown sees no need for investigation called for by David Cameron and Nick Clegg

Downing Street today ruled out an inquiry into allegations that Gordon Brown bullied staff at No 10.

The prime minister's spokesman said that Brown did not "see any need" for an inquiry of the kind demanded earlier today by David Cameron and Nick Clegg.

The spokesman also issued a new statement denying claims that Gus O'Donnell, the cabinet secretary, spoke to Brown about the way the prime minister was treating staff. The new statement went further than previous denials.

Downing Street beefed up its attempts to defend Brown in response to claims made by the Observer journalist Andrew Rawnsley and subsequently amplified by the National Bullying Helpline charity. Rawnsley said that O'Donnell was so concerned about the way Brown was treating staff that he told him to change his behaviour, and yesterday the helpline said it had received calls from staff working at No 10.

Following the publication of the Rawnsely allegations in the Observer, the Cabinet Office said it was "completely untrue to say that the cabinet secretary ever gave the prime minister a verbal warning over his behaviour".

This afternoon the prime minister's spokesman went further. "The cabinet secretary has never raised concerns with the prime minister about him acting in a bullying or intimidatory manner in relation to No 10 staff, let alone given him a verbal warning," the spokesman said.

Asked if Brown would launch an inquiry, the spokesman went on: "We do not see any need for that. The cabinet secretary has said what he has said."

The spokesman also pointed out that the head of the National Bullying Helpline made it clear earlier today that the calls her helpline received did not relate to Brown personally.

In a further attempt to rebut the allegations, Jeremy Heywood, the permanent secretary at No 10, today sent an email to staff saying that bullying was not tolerated.

"I do not believe for a moment that there's a culture of bullying and intimidation at No 10," Heywood said.

Heywood said that no organisation could afford to be "complacent" about bullying. But at No 10 there was "a deep-rooted culture of teamwork, mutual support and friendliness", he said.

Earlier today Cameron said: "These are very serious matters. I'm sure that No 10 Downing Street and the civil service in some way will want to have some sort of inquiry to get to the bottom of what has happened here.

"One way for that to happen is for Sir Philip Mawer, who is in charge of policing the ministerial code, to be asked to look into this and to find out what has been happening and get to the bottom of it."

Nick Clegg, the Liberal Democrat leader, also said the allegations needed to be investigated. "I do think this does need to be cleared up by No 10 as quickly as possible," Clegg told BBC Radio 4's Today programme this morning. "Bullying is wrong. It is totally out of order in whatever walk of life you work, however important you are."

But Brown's allies rallied to his defence. Lord Mandelson, the business secretary, said the government had more important things to do than investigate unfounded claims.

"If you think we are going to spend our time chasing around newspapers that want to splash on to their front pages allegations of this kind, just because they are relaunching and want to get the maximum publicity for what they are doing, books that need to be sold by their authors, every Tom, Dick or Harry who wants to jump up guided or otherwise by some Tory party press officer in order to pursue some smear or innuendo against the government – let me tell you, we've got better things to do in our lives."

People making allegations about Brown's behaviour needed to "put up or shut up", Mandelson said. "We need some evidence to back up this sort of claim. We haven't seen it."

Brown also received support from a more unlikely quarter when Peter Watt, the former Labour general secretary, insisted that the prime minister's behaviour under pressure fell short of bullying.

Watt, who was critical of Brown in his recent memoirs Inside Out: My Story of Betrayal and Cowardice at the Heart of New Labour, said that the prime minister's temper surfaced when he was under pressure, while at other times he could be a very supportive and loyal colleague.

"I think the term 'bullying' is a little bit emotive and possibly a little bit strong," said Watt.

Meanwhile, Jonathan Baume, the head of the FDA civil servants' union, said that ministers' behaviour too often "fell short" and that he was calling for all parties to sign up to a commitment to tackle bullying.

Refusing to be drawn into the political row over the claims that Brown acted aggressively and in a bullying manner around his staff in No 10, Baume said: "Too often politicians have little idea about what is acceptable in a modern workplace, and the behaviour of some ministers and special advisers does falls short of what is acceptable on occasions. Every government department has clear and unambiguous anti-bullying policies. In theory these should cover ministers. However, in practice no civil servant is likely to make a formal complaint against a minister. Instead, concerns about the behaviour of a minister will be dealt with through informal channels.

"If informal action does not succeed then the civil servants concerned generally either have to 'grin and bear it' whilst the minister or special adviser remains in office, or seek a transfer."

He added: "We should consider putting in place a better mechanism. All political parties could agree that their ministers and special advisers will sign up to departmental bullying codes after the general election, which set out the necessary standards of behaviour, and ask permanent secretaries to enforce codes properly."

Baume said the FDA was "struggling" to make progress in introducing an anti-bullying code in the House of Commons. "It is vital that MPs set an example in this area, and we still hope to have a code in place after the general election."

The Observer allegations became more damaging to Brown yesterday afternoon when Christine Pratt, the director of the National Bullying Helpline, said she had received calls from people working in Downing Street.

However, the NBH was dealt a blow today when one of its patrons resigned in protest at its decision to publicise allegations relating to No 10.

Professor Cary Cooper, an expert on workplace stress, said he was resigning from the NBH because he thought that Pratt had "breached confidentiality" by making such a statement.

"One of the things that is really important for any helpline or any counselling service is to retain confidentiality of the people calling up," Cooper said.

Pratt said that her comment did not breach confidentiality.