A UK industry regulator has called for the law to be changed to require pornography sites to carry out age checks before granting access.
Video-on-demand watchdog Atvod said the government must act to protect children from seeing graphic adult material.
It said credit and debit card operators would be forbidden from processing payments from British customers to sites that did not comply.
But one campaigner said the action would be a "worthless gesture".
The Authority for Television On Demand (Atvod) said the matter was so urgent that it was "critical the legislation is enacted during this Parliament".
To back up its demand, the body requested data from market research firm Nielsen, which routinely monitors the general online habits of a volunteer panel of 45,000 desktop PC and laptop users across the UK.
The survey indicated that, over the course of one month:
- 6% of children aged 15 years or younger had accessed an adult website
- 5% of visitors to such sites had been under-18
- One website alone had been visited by 112,000 boys in the UK aged between 12 and 17-years-old
- Of the wider population, 23% of those who had used the net over the month had visited an adult site
- Visitors to adult sites spent an average of 15 minutes looking at them during each visit and typically clocked up two-and-a-half hours of time in total over the month
Atvod added that the survey probably underestimated the scale of the issue since smartphone and tablet use was not included in the figures.
The regulator already forces UK-based sites to carry out age verification checks before explicit photographs and videos can be viewed.
This can be done by requiring valid credit card details, or other personal information that can be cross-referenced with the electoral roll or another ID database.
However, the body said the vast majority of online pornography was downloaded from businesses based overseas, over which it had no control.
To tackle this, Atvod said it wanted all adult sites to request a licence that would only be granted if they had age checks in place. Payment processors would be ordered not to handle fees for premium services - such as higher definition or longer clips - from UK citizens to unregistered sites.
"We're a very substantial market and to access the money that's flowing from the UK would be quite a powerful incentive to introduce restrictions," Atvod's chief executive, Pete Johnson told the BBC.
The UK government has already pressured the UK's major internet service providers to use software filters that automatically block adult material unless households specifically ask for them to be turned off.
However, a spokesman for the coalition government indicated it needed time to consider Atvod's request.
"We will continue to work with industry and others to look at where further action could be taken, including around age restrictions," he said.
Labour has, however, already come out in support of the move.
"It is only by threatening to cut off the flow of money that we will force these websites to act responsibly, and payment processors need legal clarity before they can act to help achieve this," said shadow culture minister, Helen Goodman.
However, Sex and Censorship - which describes itself as a free speech campaign group - said the move would prove ineffective.
"It won't make any difference to the sites that give all their videos away for free and sell advertising because they don't need credit card processing," said Jerry Barnett.
"And some sites are already accepting bitcoin and other anonymous online payment systems. A clampdown on card payments would just accelerate this trend.
"Even if implemented, this measure would have no effect on the range of content available to British consumers."
Mr Barnett previously ran a UK-based adult website himself until he was fined for failing to prevent children accessing its content.
Mindgeek, the Luxembourg-based operator of many of the most popular adult sites, said it already carried out age verification checks in countries where this was required. But it indicated this did not address the crux of the problem.
"There is no single 'silver bullet' solution to protecting children and adolescents from potentially harmful content and interactions in their digital lives," said a spokeswoman.
"The best solution lies in a multi-layered approach in which the parent assumes the central role."
Atvod acknowledged its proposal was only part of the solution, but it insisted that the scheme could still be designed to make a difference.
"The material that appears on the free services is placed there by the paid services to attract customers to sign up to subscriptions.
"As long as the paid service placed content on a free service without age verification it would be in breach of its licensing conditions and so would not be able to access funds from the UK.
"We're not saying this will stop all children seeing all pornography online.
"But our argument is that even if you reduce the number of children who are accessing hardcore pornography online by 10%, that would be a significant win."