Digital Minister Margot James has apologised for the six-month delay on the so-called "porn block", which had been due to take effect on Monday.
It is designed to force pornography websites to verify users are over 18.
But the law has been delayed twice - most recently because the UK government failed to properly notify European regulators.
"I'm extremely sorry that there has been a delay," Ms James told the BBC. "I know it sounds incompetent."
She added: "Mistakes do happen, and I'm terribly sorry that it happened in such an important area,"
Under the proposed rules, the British Board of Film Classification (BBFC) would supervise the compulsory age checks. Websites which fail to comply would be blocked by internet service providers.
Only websites where more than a third of content is pornographic are covered - which excludes social media sites.
But critics say how exactly the scheme will work is still unclear. Some options include uploading copies of a passport or driving licence, or buying vouchers from local shops.
It was originally supposed to take effect in April 2018, but was delayed to provide time to "get it right".
"I think it's outrageous," said Sarah Wollaston, chairwoman of the Health and Social Care Committee
"It's another example of the government failing to protect children and young people. I'm afraid everything in this place is being kicked down the road because of the delays caused by the leadership election and the Brexit process."
Dr Wollaston was a party colleague of Ms James until she resigned from the Conservatives in February. She is now an independent.
'A fox in charge of the hen house'
Some have also questioned whether one of the main providers of age verification software has a potential conflict of interest.
Mindgeek, the largest such company, also owns some of the world's largest pornography sites, including Pornhub.
Dr Wollaston said it was the equivalent of "putting a fox in charge of the hen house".
"I think Mindgeek's intention is to own the market and make all the money," said Jim Killock, executive director of digital rights group Open Rights. "I don't see that it's got much other motivation, at the end of the day."
The company strongly refutes such suggestions.
"It's not in our or our advertisers' interests to have children visiting our sites - so there's no conflict of interest," it said, stressing that its sites "neither aim to market to nor target minors on any level".
Ms James said such a conflict would only be a problem if the firm had a monopoly on age verification.
"I agree they're the largest player in it, but there are other age verification providers.... so I think that we feel like that's acceptable," Ms James said.
But Mr Killock warned that the company's involvement had other potential impacts.
"Pornhub and Mindgeek are going to be able to get a birds-eye view of the whole industry, of all of the adult users," he said.
This could allow them to "see exactly what kind of content they should be selling next, which websites they might want to buy".
"That level of market intelligence and market power and personal information has been handed to them on a plate by the UK government, because it has refused to regulate what these tools should be, how they should work," he said.