Viewers and listeners are rallying around the BBC, according to a Guardian/ICM poll published today. It shows rising levels of trust in the broadcaster and increased public support for the licence fee.

The results challenge claims that the BBC's growth has a "chilling" effect on consumer choice, made last month in a speech by James Murdoch, European chief executive of News International. His comments opened up debate about the future of the corporation, which is protected by its guaranteed licence fee while some other media organisations are facing sharp falls in revenue.

Murdoch criticised what he called the "expansion of state-sponsored journalism" on the BBC's website, but today's poll suggests public respect for the BBC's output is growing.

An overwhelming majority, 77%, think the BBC is an institution people should be proud of – up from 68% in an equivalent ICM poll carried out five years ago. Most, 63%, also think it provides good value for money – up from 59% in 2004.

Since the previous poll the BBC has come under fire for the standards of its journalism, after the Hutton inquiry and during the scandal involving fake phone-in competitions on high-profile programmes and wrongly edited footage of the Queen.

But public confidence in the corporation's output has grown. Asked if the BBC is trustworthy, 69% now say yes, against 60% in 2004. Only 26% disagree.

Confidence in the BBC has also improved sharply since a Guardian/ICM poll in 2007. Then, a majority, 59%, said their trust in the corporation had fallen in the wake of the much-publicised TV fakery scandals, while only 37% said it was unchanged.

Now attitudes have reversed. A majority, 57% say their trust in the BBC has not faltered while 41% say it has fallen.

The BBC seems to have overcome criticism of the high salaries paid to some members of staff and stars such as Jonathan Ross. Only 49% think the BBC should declare what it pays people, against 50% who do not.

This show of public support comes during a difficult year for the BBC, in which it has faced concerted criticism from politicians, sections of the national press and rival media companies over levels of executive and talent pay. The BBC responded in June by revealing the pay and expenses of senior executives, but has been fighting a rearguard action against mounting pressure to publish more details of the pay of top presenters such as Jonathan Ross.

The BBC is also involved in a political tussle over the future of the licence fee. The government's Digital Britain report in June recommended that a portion of the licence fee be set aside for funding a replacement for ITV's regional TV news service and children's programmes on Channel 4, a move that the BBC is fighting vigorously to prevent.

Support for the BBC sits alongside strong continued respect for other broadcasters, including Sky, part-owned by News International.

Asked whether they think the BBC is more likely to tell the truth than its rivals, only 38% agree. A clear majority of viewers and listeners – 58% – said they think there is no difference between news on the BBC and other channels. Those figures are almost identical to results from 2007.

Most people also question the continued need for the licence fee – although support for it has risen over the last five years. Asked to pick from a range of ways of funding the BBC, including the licence fee, a subscription service and selling advertising, more people back the licence fee than any alternative.

But supporters remain in the minority. The fee is backed by 43%, against 24% who think advertising should foot the bill and 30% who think people should pay to subscribe if they want to see BBC programmes. In 2004, only 31% backed the licence fee, 12 points lower than today.

In other areas, opinions are contradictory. Most people – 81% – think the BBC should stay impartial in return for its right to raise money.

But there is also public support for Murdoch's call for the easing of tight restrictions on what broadcasters can say: 61% agree the BBC and other broadcasters should be free to hold political positions, against 37% who disagree.

Nor is there any demand for the BBC to ease pressure on commercial rivals by charging for its website. Only 16% think this should happen, against 79% who do not.

However many people think that the BBC has dumbed down since its heyday. While 57% think it has gone downmarket, 40% do not.

ICM Research interviewed a random sample of 1001 adults aged 18+ by telephone on 2-3 September. Interviews were conducted across the country and the results have been weighted to the profile of all adults. ICM is a member of the British Polling Council and abides by its rules.