Molly was 14 when she took her own life in 2017 after being exposed to self-harm content online.
Burrows said that parents across the country were looking for “decisive action” from the government and the introduction of “measures that can actually succeed”.
This could include enforcing tougher restrictions on features which make social media addictive, such as banning autoplay, infinite scroll, and the algorithms that “bombard” children with harmful material.
He said these features contributed to the harm that led to Molly’s death.
Burrows said that experts and organisations working on child safety “do not have confidence” in an Australia-style ban for under-16s.
Australia introduced the ban in January, but in March, its eSafety Commission found that seven in 10 parents whose children already had a social media account said they were still on the platforms.
Burrows told BBC Breakfast: “In Australia this is not working, it’s not something that is enforceable.”
He added: “This looks like policy making being done on the back of a fag packet and frankly that is incredibly high risk when we are talking about children’s safety. We should be following the evidence.”
The UK government announced a consultation on children’s social media use in January, to examine the most effective ways to ensure young people can remain safe online.
It received 116,211 responses.
Government ministers have examined a variety of options for restrictions, including a blanket ban or the introduction of screen time limits.
Proponents of a ban have been offering “false hope” to parents, Burrows argued. “I’m looking at all the evidence, the sector is looking at all the evidence, and we just don’t see what lessons we can learn from Australia.”
Ian Russell, Molly’s father, told BBC’s Newscast in January that the government should enforce existing laws rather than “implementing sledgehammer techniques like bans”.