No 10 has called on social media companies to go further to remove unacceptable content from their platforms following the death of the television presenter Caroline Flack.

ITV went ahead with its reality TV show Love Island, which Flack previously hosted, on Monday night after a two-day hiatus.

The episode began with a tribute to Flack by narrator Iain Stirling, who praised her “passion, warmth and infectious enthusiasm”. Stirling said: “We are all absolutely devastated by the tragic news that Caroline, a much loved member of our Love Island family, has passed away.”

He added: “Like many of you right now we are all just trying to come to terms with what has happened. My only hope is that we can all try to be kinder, always show love and listen to one another.

“Caroline, I want to thank you for all the fun times we had making our favourite show. You were a true friend to me. I’m going to miss you, Caz.”

Boris Johnson’s deputy official spokesman said Flack’s death was a “tragedy”, adding “our thoughts are with her family and friends at this very difficult time”.

Politicians have condemned press intrusion, calling for more regulation of both traditional and social media after the death of Flack, who is understood to have taken her own life on Saturday at her home in London. She had been charged with assaulting her partner and was due to stand trial in several weeks’ time.

Asked for the prime minister’s view on social media bullying and press intrusion in light of Flack’s death, he said: “The industry must continue their efforts to go further. We expect them to have robust processes in place removing content breaching their acceptable use policies.” His answer appeared to be referring to social media companies rather than the press.

The spokesman declined to comment on ITV’s decision to pull episodes of Love Island and said the decision to charge Flack – even though her partner did not support the prosecution – was a matter for the Crown Prosecution Service.

After Flack’s death, the companion programme Love Island Aftersun – which was due to air on Monday at 10pm on ITV2 – was also cancelled.

Explaining the decision to air the main programme, Kevin Lygo, director of television at ITV, noted that it would include a tribute and said: “Caroline loved Love Island and was very vocal in her support of the show. Viewers could relate to her and she to them and that was a big part of the programme’s success.”

Lygo also said that the possibility of Flack’s return to the show had remained open, saying: “After Caroline stepped down from the show ITV made it clear that the door was left open for her to return and the Love Island production team remained in regular contact with her and continued to offer support over the last few months.”

Aftersun, usually broadcast on a Monday night directly after Love Island, is hosted by Laura Whitmore, who spoke of her affection for Flack and called on listeners to “be kind” during her BBC Radio 5 live show on Sunday.

“Caroline loved to love, that’s all she wanted, which is why a show like Love Island was important to her, because the show is about finding love, friendship and having a laugh,” Whitmore said. “The problem wasn’t the show. The show, to work on, is loving and caring and safe and protected. The problem is the outside world is not.”

The cancellation of the Aftersun programme, which is filmed live in front of a studio audience in the UK and features panel discussions and games, follows ITV’s decision to pull Saturday’s omnibus Love Island: Unseen Bits and Sunday’s episode of the main show.

On Monday ITV and the show sponsor Just Eat also said the regular idents that run on the show would be dropped and replaced with information on sources of support for viewers affected by Flack’s death.

It has been widely reported that contestants currently competing in the show – which finishes next Sunday – have not yet been told about Flack’s death. ITV has been approached for comment but is yet to respond.

The Labour leadership contender Keir Starmer criticised mainstream outlets for “amplifying” damaging social media posts about Flack, and signalled he would take action to “diversify” the press if he won the race to succeed Jeremy Corbyn.

The former director of public prosecutions said the presenter’s death “shocked a lot of people”, adding: “It wasn’t just social media, it was the media amplifying what social media was doing. It was both strands. There is a human impact.

“The press more widely have to take responsibility as well. Not just for the hatred and abuse but for the vilification constantly of Labour MPs and Labour leaders. We have got to do something to diversify our press, to have a better media.”

His fellow leadership contender Lisa Nandy said social media companies could not be left to police themselves, suggesting the current situation was like the “wild west”.

“I worry about the approaches that say we allow the social media companies to regulate themselves,” she said. “In no other area of life would we allow private companies to police themselves. We ought to make sure the state has a system of regulation and support around that.”

The transport secretary, Grant Shapps, in a media round on Sunday on behalf of the government, referred to the results of the online harms white paper consultation, which looked at ways of better protecting children and vulnerable people.

Shapps said he did not know the full circumstances of the case but said the Crown Prosecution Service had a duty of care.

In the UK and Ireland, Samaritans can be contacted on 116 123 or email jo@samaritans.org or jo@samaritans.ie. In the US, the National Suicide Prevention Lifeline is 1-800-273-8255. In Australia, the crisis support service Lifeline is 13 11 14. Other international helplines can be found at www.befrienders.org.