Shadow Culture Secretary Tracy Brabin rounded on the newspaper industry over it treatment of the television host, who was found dead at the age of 40 at her home in east London on Saturday, after taking her own life.
Miss Flack, who was described as "vulnerable" by her management, had pleaded not guilty to assaulting her boyfriend Lewis Burton at her former flat in north London in a court hearing in December.
The shock news of her death prompted a flood of tributes from celebrities. But it also brought questions about the decision to persist with prosecuting her for the alleged assault on her boyfriend, and about the pressures faced by TV celebrities from the press and social media.
Her management company criticised the Crown Prosecution Service (CPS) for pressing ahead with what it called her "show trial" even after her boyfriend said he did not support it.
By Sunday evening, an online petition calling for a Government inquiry into "the practices and policies of mainstream media organisations and social media platforms in their efforts to protect members of the public from harm" had more than 200,000 signatures.
Ms Brabin, the Labour MP for Batley & Spen, told the BBC Radio 4 Westminster Hour: "There's been a lot of blame-gaming, people blaming ITV, people blaming the press.
"This is why the Labour Party were pressing for Leveson 2, because it does feel like after everything that we went through we still are back at that place again where celebrities are being hounded by particular news outlets and their private life is being splashed across the front pages.
"I do think it's important that we press social media but also newspapers don't get away with it either."
The Government's Leveson inquiry into press ethics, which last sat in 2012, was chaired by Sir Brian Leveson and was set up by David Cameron following the phone-hacking scandal.
Plans for it to move on to a second phase focusing on media relations with the police were scrapped by Theresa May. Calls for it to be reconstituted were led by the former Labour leader Ed Miliband.
Caroline Flack stepped down from presenting the current winter series of Love Island after the alleged assault of her boyfriend. The ITV programme did not air on Sunday night, but will be back on today with a tribute to Flack.
The tragedy has put the spotlight back on the pressures which come with TV celebrity.
Flack is the fourth person linked to the ITV2 dating programme to have killed themselves.
Sophie Gradon, who was a contestant in 2016, was found dead at her home in 2018 at the age of 32. Her boyfriend Aaron Armstrong, who had found her body, killed himself three weeks later. He was 25. Mike Thalassitis, who appeared in the 2017 series, was 26 when he was found dead in a park in March last year.