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The Duke of Cambridge has accused social media firms of not being proactive enough about dealing with fake news, privacy issues and cyber-bullying.

In a speech given at the BBC, Prince William said social networks had allowed "misinformation and conspiracy to pollute the public sphere".

"Their self-image is so grounded in their positive power for good that they seem unable to engage in constructive discussion about the social problems they are creating," he warned.

The prince and the Duchess of Cambridge had been invited to the BBC to try out a new internet safety app.

During their visit, the royal couple met children and their parents who had helped design it.

"The tools that we use to congratulate each other on milestones and successes can also be used to normalise speech that is filled with bile and hate. The websites we use to stay connected can for some create profound feelings of loneliness and inadequacy," said the Prince in his speech.

The prince said tech firms had a "great deal to learn" on responsibility.

"Social media companies have done more to connect the world than has ever been achieved in human history. Surely you can connect with each other about smart ways to deal with the unintended consequences of these connections," he said.

"You can reject the false choice of profits over values. You can choose to do good and be successful."

The BBC put the prince's criticism to Facebook's chief executive Mark Zuckerberg.

He said part of the challenge was figuring out how to balance the privacy users wanted against a desire to do more to crack down on bad behaviour.

"I do think there's some trade-off on some of these issues between privacy and some of the safety work," Mr Zuckerberg said.

"A lot of what we are trying to do is architect the systems to give people really good privacy too.

"This is why these are big and important questions, and why broadly across society people don't necessarily agree on actually where you should draw the line."

Another executive added that Facebook was using artificial intelligence to root out unacceptable behaviour, but it was harder to identify cases of cyber-bullying than other problems because the nature of the messages involved was so personal.

Analysis: Leo Kelion, technology desk editor

Image copyright Getty Images Image caption Prince William and Catherine met parents and children at the BBC

This is far from the first time The Duke and Duchess of Cambridge have spoken out about cyber-bullying.

They launched a taskforce to tackle the problem in June 2016, which involved Facebook, Snapchat and Google among others.

They have returned to the issue since, but this does represent a change of tone.

Rather than focusing on co-operation, this time the prince accused the tech leaders of posturing, being too proud and defensive, and having put their shareholders' interests above those of their users.

Moreover, the prince said he was "disappointed" that the taskforce he had built had failed to achieve more.

For Facebook in particular, this couldn't come at a worse time.

The firm has been beset by data breach scandals, claims its products encourage loneliness and depression, and evidence its apps have been used to meddle with elections.

And on Wednesday, the New York Times published a fresh series of claims about dubious backroom tactics as the social network tried to fight back against all the negative publicity.

During a lengthy press conference this evening, chief executive Mark Zuckerberg acknowledged that there had been a lot of issues his firm had been behind on and that "a lot of the critique of the company is fair".

But he said that he was "very clearly involved" in addressing users' concerns and pointed to an essay he had just published to update them on his efforts.

He added, however, that he and his team could not "snap our fingers" and resolve all the complaints quickly - rather it would likely take years.

The dangers for Facebook are that its members may not be willing to stick around that long and that politicians may feel the need to introduce tougher regulations in the meantime.

The BBC is a member of an industry-wide taskforce set up by the prince to tackle cyber-bullying.

After being greeted by excited crowds outside the BBC studios in central London, the royal couple were pictured with BBC director general Tony Hall and the director of BBC Children's, Alice Webb.

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Image copyright Getty Images Image caption Alice Webb (left) and Lord Hall (second left) hosted the royals for their visit to the BBC

Image copyright PA Image caption The royals tried out an app designed to tackle online bullying

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During Thursday's brief visit, the couple also met young people who wrote and performed a new video for a campaign run by the Prince's cyber-bullying taskforce.

The campaign, called "Stop, Speak, Support", involves a national code of conduct for children on what to do if they come across bullying online.

Image copyright Getty Images Image caption The royal couple also met Radio 1 breakfast show presenter Greg James, who has changed job since their last visit to the BBC

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Image copyright BBC RADIO 1

It is not the first time the royal couple have visited the BBC - in 2017 they dropped in on Radio 1 and helped read the UK's Official Chart with Greg James.

And the Queen visited the BBC in 2013, when she was shown around the main newsroom.