The policy would have required all adult internet users wanting to watch legal pornography to prove they are over 18 by providing some form of identification.
Colin Hart, Director of The Christian Institute, said: "This is a big victory for pornographers and the campaign of the Adam Smith Institute.
"It's a warning for Christians about the values of the libertarian right.
"Their influence could also lead to other radical changes like the legalisation of drugs.
"As the sociologist the late Norman Dennis pointed out on family values there is very little to choose between the 'egotistical left' and the 'libertarian right'."
Legislation on age-verification was mooted by David Cameron in 2015. The Digital Economy Act – containing the checks – was passed in 2017 but the age-verification aspect was postponed in April 2018 and again in June this year.
The checks would have required users to prove their age using a credit card or passport.
Users would also have been able to buy an over-the-counter access card from shops, where age-verification could take place face-to-face.
Online pornography sites that refused to follow the regulations would have been blocked by UK internet service providers.
The Adam Smith Institute claimed the plan would 'infringe freedom' and would "reduce access to pornography produced for sexual minorities".
Nicky Morgan, the digital secretary, insisted, "the government's commitment to protecting children online is unwavering," in a statement revealing the climb down.
Websites that refused to implement the checks faced being blocked by UK internet service providers or having their access to payment services withdrawn.