The policy was supposed to launch in April 2018 but didn't after repeated delays because of criticism that it wouldn't be effective.
CARE's Chief Executive, Nola Leach said she's "desperately disappointed" that the Government has ditched the proposals.
"The Government promised age-verification in its 2017 election manifesto so to suddenly drop it like this is extraordinary and outrageous," she said.
"The simple fact is our children and young people are not as well protected online as they are offline.
"Children as young as seven are stumbling across porn online and it is absolutely right that we should be doing everything we can to protect them. Today's announcement is a betrayal of our young people."
Critics of the age-verification policy warned what that making people prove their age before entering porn sites could cause privacy issues and under-18s could easily bypass the restriction using virtual private networks (VPNs).
In a written statement, Nicky Morgan, Secretary of State for Digital, Culture, Media and Sport, said the government is still concerned about the prevalence of adult content online and believes it's vital that children are protected from accessing inappropriate, harmful content.
She said that protecting children from such sites will be better achieved in other ways which were published in the Online Harms White Paper in April 2018. Part of the new plan is to focus on keeping web firms accountable on how they protect young people.
As a consequence, the government "will not be commencing Part 3 of the Digital Economy Act 2017 concerning age verification for online pornography," she said.
"The Digital Economy Act objectives will therefore be delivered through our proposed online harms regulatory regime. This course of action will give the regulator discretion on the most effective means for companies to meet their duty of care. As currently drafted, the Digital Economy Act does not cover social media platforms."
Leach said she wished the government would take a stronger stance against the issue.
"This Government could have led the way in the world in driving this forward, other countries were watching to learn from our experience of doing so," she said.
"Now all the time and effort to make age-verification a reality has been wasted.
"CARE has done polling which showed the proposals were supported by a majority of the public so there is no logic in just giving the scheme up."
The age-verification plan was most recently delayed in June after the government failed to notify European regulators about the policy.
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