The BBC has given the first hint of a U-turn over plans to close its digital radio station BBC 6 Music, after a furious backlash from listeners, trade unions and some of its own staff.

The proposed closure of 6 Music, along with its sister digital station the Asian Network, was confirmed by the BBC today as part of a wide-ranging strategy review by its director general, Mark Thompson.

Half of the BBC's web pages will be shut and £100m will be saved from overhead costs as part of a package of cuts intended to free up £600m a year to be reinvested in high-quality content. The proposals also include cutting spending on foreign shows such as Mad Men by 20%, capping investment on sports rights and potentially selling off BBC magazines such as Top Gear.

But BBC Trust chairman Sir Michael Lyons said that if there was a big enough public response about the cuts, he would ask management to rethink its strategy.

"If we find that... there's massive public concern that we need to take account of then we will go back to the director general to rethink the strategy before it's approved," he said. The proposals will now be the subject of a 12-week public consultation by the Trust.

The BBC has committed to spending at least 90% of the licence fee on "high-quality content and distribution" by 2013. Within that 90% guarantee, at least 80% of the licence fee will be spent on "content creation".

The broadcasting trade union Bectu claimed the cuts could lead to another 600 job losses at the corporation, which has seen more than 7,000 jobs go in the last five years. Its general secretary, Gerry Morrissey, described the cuts as "totally unnecessary and purely politically motivated".

Thompson described his review as a "step change" in the BBC's history. "These are difficult decisions and it's painful for the people who listen and watch a given service and for those people that broadcast it," he said.

"I don't want to pretend that these are easy decisions. It's very interesting that politicians say: 'Why don't you cut these services?' When we start doing that, they say: 'Have you gone mad?' This is a moment for focus and rationalisation after a period of very broad growth of activities across the BBC."

Confirmation of the decision to axe the eight-year-old music station 6 Music – it is due to stop broadcasting at the end of next year – prompted an angry response from the station's listeners. About 90,000 people had joined the Facebook group "Save BBC 6Music" by the end of yesterday.

Jeremy Dear, general secretary of the National Union of Journalists, said Thompson had put BBC management "on a collision course not just with us and the hundreds of BBC staff who face losing their jobs, but with licence fee payers up and down the country.

"If the BBC has to look at savings, they should tackle executive pay rather than programmes or content."

Lyons said: "The public pick up the bill for the BBC and it is right that it constantly evolves to meet their expectations. We welcome the general direction of this report, although we will want to test and consider how it is delivered. We are clear it heads towards a more disciplined and sharply focused BBC. That will mean some difficult choices. But we will not shrink from those choices where they are in the interests of licence fee payers."

BBC Radio 5 Live presenter Richard Bacon, who also has a show on 6 Music, was one of the BBC presenters to publicly speak out against the decision to shut the station.

"6Music is staffed by talented people providing 'distinctive' programming that values 'quality over quantity'. Exactly what this restructure is supposed to be about," he said.

"6Music is distinctive and serves an audience not catered for by the commercial sector. What happens when folk use whatever rationale they have come up with to justify the 6Music decision and apply it to other parts of the BBC?" said Bacon on Twitter.

DJ Lauren Laverne, mid-morning presenter on 6 Music, said listeners' messages about the closure of the station had reduced her to tears. "Worst walk to work ever. Like that final trip to the vet's," she tweeted. "Most emotional day at work of my life."

Liberal Democrats culture spokesman Don Foster accused the BBC of using 6 Music and the Asian Network as "sacrificial lambs". "Today's report signals the end of the BBC roaming wherever it fancied. The decision to focus on high quality UK content is welcome," he said.

"However, I am not convinced that using 6 Music and the Asian Network as sacrificial lambs to pay for it is the right approach. While the BBC has become overgrown in some areas and needs pruning, the licence-fee-payers must have their say about what's to go."

The decision to close the Asian Network was criticised by Professor Daya Thussu, director of the London-based India Media Centre, part of the University of Westminster, who said the closure showed the BBC was "abandoning its inclusive agenda and thus compromising its public service remit".

"The closures show that the BBC is abandoning its inclusive agenda and thus compromising its public service remit. The demise of the Asian Network would make the BBC less multi-cultural and, to borrow an apt phrase from one of its former bosses, more 'hideously white'."

The culture secretary, Ben Bradshaw, said the BBC was a "great British asset and should not approach the future assuming the Conservatives, who are viscerally hostile to the BBC, will win the election". He warned against politicians "compromising the BBC's independence by giving a running commentary on its decisions".

The shadow culture secretary, Jeremy Hunt, said he wanted to see "actions not words" from the corporation. "I am pleased that the BBC is taking a long hard look at exactly what it should be doing ... Will the BBC be less expansionist? Will it think carefully about its impact on the independent sector? Above all, will it spend licence fee payers' money on quality public service content that they want to see?"

The closure of 6 Music and the Asian Network is a blow to the radio industry's efforts to go digital. The two stations had around a million listeners between them.

But Ford Ennals, chief executive of digital radio switchover body Digital Radio UK, remained upbeat. "Whilst some listeners will inevitably be disappointed by the closure of individual services, we believe the BBC's vision as outlined in the strategic review will ultimately result in greater levels of overall listening to digital radio."

BBC2 will be one of the main beneficiaries of the decision to plough more money into programming, with a £25m increase in its programme budget from 2013. Children's programming will see a boost of £10m each year, but the BBC intends to leave the teen market to rivals such as Channel 4 and has proposed the closure of BBC Switch and Blast!.

The BBC said that it aims to cut spend on imported programming by 20% from a budget of £100m today and to cap it at a maximum of around £85m a year in the future. Sports rights expenditure, on events such as Wimbledon and Formula 1, will be capped at about £300m a year.

The BBC's internet operation will see the number of web pages it publishes halve by 2013. The scaling back of the web operation will include an approximate 25% cut in budget and similar slashing of staff numbers, potentially affecting as many as 350 employees. Regional newspaper groups will be buoyed by a commitment to curtail local activities including a promise to "never be more local" than it is now.

The BBC also said that during the next licence-fee period, from 2013 to 2016, Thompson will be made personally responsible for reducing the corporation's overheads bill from about £410m to just over £300m per year – from 12% of the licence fee to 9%.

The report states that the corporation must go further than previously announced cuts to senior management levels and pay, details of which were announced last October, with further reductions in costs associated with top talent, property and distribution. The report also said that the traditional BBC hierarchy needed to be given a "flatter, more dynamic and flexible structure". It said that the BBC needed to make a "step change" in simplifying its operations and structure.

Last week the National Audit Office criticised the BBC for overspending by more than £117m in three construction projects.

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