* Conservative support slumps to lowest since 2004
* Cameron denies offering BSkyB favours to media tycoon
* Cardinal says UK govt economic policy is "immoral"
By David Milliken
LONDON, April 29 (Reuters) - British Prime Minister David Cameron has denied favouring Rupert Murdoch's business interests in exchange for political support from his newspaper empire, and defended a minister's handling of an ill-fated takeover bid involving the media magnate.
Cameron is on the back foot ahead of local elections across much of Britain on Thursday. After a month of bad headlines about Murdoch, the budget and the return of the economy to recession, an opinion poll registered support for his Conservative Party at its lowest since 2004.
In a television interview on Sunday, Cameron said there had been no deal with Murdoch to nod through NewsCorp's attempted takeover of Britain's biggest satellite TV firm BSkyB in return for support at the 2010 election that brought him to power.
"The idea of some grand bargain between me and Rupert Murdoch, that is not true," Cameron told the BBC. "I do not do things or change my policies to suit this proprietor or that proprietor. That is not the way I work, and I will say that under oath."
An inquiry into phone-hacking by Murdoch's newspapers, led by the judge Brian Leveson, has revealed the formerly close links between Murdoch and the British government.
An adviser to Jeremy Hunt, the media and culture secretary who had overseen the BSkyB bid until Murdoch withdrew it in July, resigned on Wednesday after emails emerged showing he had been in close contact with NewsCorp about the deal.
Now the opposition Labour Party is pressing Hunt to resign, saying Cameron must launch a separate inquiry into whether Hunt himself breached rules on ministerial conduct.
However, Cameron said he saw no evidence that Hunt had overstepped the line of propriety and there would be no separate inquiry unless Hunt's testimony to the Leveson inquiry revealed new facts. "As things stand I do not believe that Jeremy Hunt breached the ministerial code," Cameron said.
Asked if he was still 100 percent behind Hunt, Cameron said that Hunt - who is also responsible for the 2012 Olympic Games in London this summer - was doing a good job, and had not yet had the opportunity to defend himself.
"I think he is a good culture, media and sports secretary. I think he is doing an excellent job on the Olympics. If someone has breached the ministerial code and behaved badly, they can't stay in the government. But they should be able to defend themselves."
On Friday Leveson refused to bring forward the date of Hunt's testimony, which is several weeks away.
Labour finance spokesman Ed Balls, speaking to Sky News after Cameron's interview, said that Cameron should stop trying to defend Hunt.
"If the prime minister put the same energy into defending hundreds of thousands of jobs up and down the country as he is into Jeremy Hunt - one person in his cabinet - then he might not be losing trust so quickly."
Support for the Conservatives has fallen to 29 percent while Labour is on 40 percent, according to a YouGov poll in the Sunday Times newspaper.
Cameron has been attacked even within his own party for appearing out of touch after a budget in March that cut income tax for the richest Britons while raising taxes for retired people and on everyday items such as hot pies known as pasties.
On Sunday, Scotland's most senior Roman Catholic, Cardinal Keith O'Brien, said Cameron had failed in his moral obligation to consider the poor.
"It is these people who have had to suffer because of the financial disasters of recent years and it is immoral," the cardinal told the BBC. "It is not moral just to ignore them and to say 'struggle along', while the rich can go sailing along in their own sweet way."