Labour has promised to give bereaved families access to their children’s social media “as fast as possible” if it wins the election.
Shadow home secretary Yvette Cooper said that “urgent action” was needed.
In February it was reported that plans were underway to allow coroners to demand internet giants hand over data to inquests into the circumstances of a child's death.
Campaigners have been pushing for new powers after the case of Molly Russell, a 14-year-old who ended her life in November 2017 after viewing suicide and self-harm content online.
The coroner in her case concluded that the schoolgirl died while suffering from the "negative effects of online content".
Asked about plans to entitle bereaved parents to access to their children’s data on their mobile phones or tablets on the BBC’s Sunday with Laura Kuenssberg programme, Ms Cooper said: “We do need to pursue this. And there’s a series of areas where we need really quite urgent action around online safety, around implementing online safety measures”.
Asked if Labour would bring in the powers straight away, Ms Cooper said: “As fast as legislation is possible.”
Her stance was backed by the health secretary Victoria Atkins.
She said the issue had to be decided collectively by her party but added: “If it was up to me alone it would be a big ‘yes’.”
Earlier this year the science secretary Michelle Donelan said the Tory party’s plans would be an “important change (that) will give bereaved parents access to critical digital information at a tragic time.
"Although nothing can take away the pain endured by the families, I hope this amendment goes some way to give more answers to anyone unfortunate enough to find themselves in similar heart-breaking situations."
Baroness Kidron, a crossbench peer who campaigns for more protections for young people online, has said that transparency is necessary to “lift a veil on the role of tech companies” in cases where children die and that the information “however painful, is necessary for parents to come to terms with the death of their children”.