Baroness Howe has voiced concerns that Tesco Mobile is not automatically filtering adult content for new mobile phone purchases, despite David Cameron's assurances earlier this year that such content would be blocked.
The debate in the House of Lords during which Baroness Howe made the revelation also brought to light the fact that an estimated one million households remain unprotected by the internet self-regulation promoted by the Prime Minister.
This could account for two million children having the possibility of being exposed to explicit internet sites.
Mr Cameron moved earlier this year to make internet service providers automatically implement filters on new broadband connections and ask existing customers if they would like to opt-in to the filter system.
The change is in response to growing evidence that approximately a third of children in the UK will have accessed pornography by the time they are ten years old.
It has been supported by providers such as BT, Virgin Media and TalkTalk, with the Prime Minister describing the move as "real progress" for parents.
However, the agreement between the Prime Minister and the industry is voluntary, with an estimated five per cent of the market still uncovered.
Baroness Howe's proposed Online Safety Bill would place a statutory obligation on all internet service providers and mobile phone operators to provide an internet service that is adult-content free with access subject to age-verification.
Unlike the current system, the change would cover a hundred per cent of both the internet and mobile market.
"My Bill goes further than the Prime Minister has done so far. It introduces the missing element of legislative compulsion so that the industry really does make child internet safety a priority," she said.
"What we require is a robust system that affords children the same legal protections online as they enjoy offline."
The current voluntary approach to regulating the internet requires parents to actively choose to setup filters against pornography.
However, the advocacy charity CARE, which is backing the Bill, said this approach is weak.
It has reiterated its call to make web filtering a legal requirement.
Nola Leach, Chief Executive of CARE, said, "Mobile phone operators and internet service providers need to be compelled to take action to protect children online by a change in the law.
"The case of Tesco Mobile shows that a voluntary approach is not working and as a result children are being exposed to sexually explicit material that the Prime Minister wrongly assured their parents they'd be safe from.
"The Online Safety Bill before Parliament has CARE's full backing."