The government is considering further action to keep children safe online and will not “sit back and wait” on the issue, a cabinet minister has said.

Transport Secretary Heidi Alexander told the BBC new age-verification rules beginning later this month would have a “really important” impact.

She said the regulations, to be overseen by media regulator Ofcom, would not be the “end of the conversation” on online safety.

Ofcom boss Melanie Dawes vowed to rigorously enforce the new requirements, adding the regulator “means business”. But she acknowledged Ofcom may require further legal powers in order to keep pace with the rapidly developing impact of artificial intelligence (AI).

Under new powers introduced by the Online Safety Act and passed under the previous Tory government, Ofcom will require internet companies to conduct stricter age verification methods to check whether a user is under 18.

A new code of practice, to apply from 25 July, will also require platforms to change algorithms affecting what is shown in children’s feeds to filter out harmful content.

At the last election, Labour committed to “build on” the previous government’s law and consider further measures to keep children safe.

But it is yet to publish fresh legislation of its own, with ministers arguing the existing set of new regulations need to be rolled out first.

Speaking to Sunday with Laura Kuenssberg, Ian Russell, whose daughter Molly took her own life at 14 after seeing harmful content online, said the new rules should mark the “biggest moment in online safety” since the arrival of social media.

But he added the “proof of the pudding is in what happens,” adding he thought Ofcom could go further than it has done within the legal powers it has acquired.

He also argued that the regulator should be prepared to “push back” against ministers over “weaknesses” in the legislation.

Alexander said the new rules would bring in “really robust safeguards” to ensure proper age verification.

But she added: “We are very clear as a government that this is the foundation for a safer online experience for children, but it is not the end of the conversation”.

She said Technology Secretary Peter Kyle was looking at further action in a number of areas, including how to address “addictive habits” among children.

“We’re not going to be a government that sits back and waits on this, we want to address it,” she added.

She did not provide further details, but Kyle has previously indicated he wants to curb the “addictive nature” of apps and smartphones for children.

Proposals under consideration include a two-hour cap on the use of individual social media apps, and a 22:00 curfew.

Alexander added that the education secretary was reviewing guidance in England that allows individual headteachers to ban smartphones in schools.

The government has so far stopped short of legislating for a nationwide ban, voting down a Tory attempt to do so in March.

The transport secretary added that it was important to “get the balance right” on the issue, noting that some parents “want their kids to have a phone on their way to school”.

Shadow minister Chris Philp said he wished the previous Tory government had legislated to ban smartphones in schools during its 14 years in power.

He told Kuenssberg it was a “great shame” Labour had not backed a ban, adding: “As a dad myself, I am really concerned about this”.

Ofcom’s chief executive told the programme the new rules would mean tech platforms would have to change their content algorithms “very significantly”.

Ms Dawes said the regulator would give websites some flexibility when deciding which age-verification tools to use, but pledged that those failing to put adequate checks in place “will hear from us with enforcement action”.

However, she acknowledged some newer forms of AI “may not” be covered be powers contained in the existing legislation.

“There may need to be some changes to the legislation to cover that,” she added.