Originally, the government had hoped to introduce the controversial amendment in April, but the Department for Digital, Culture, Media and Sport has confirmed that it would now start "later in the year".
In a statement, Myles Jackman - the Open Rights Group's legal director - responded to the news by saying: "This is a chance for the government to rethink the absence of safeguards for privacy and security, but it is frightening to consider that this policy was two weeks away from launch before it was pulled.
"[The government] needs to introduce powers to safeguard privacy immediately before this scheme causes real damage."
When the plans were first announced, Digital minister Matt Hancock said that the change will make a huge difference to child protection in the UK.
At the time, he explained: "All this means that while we can enjoy the freedom of the web, the UK will have the most robust internet child protection measures of any country in the world."
The move was also welcomed by Will Gardner from the internet safety charity Childnet.
He said: "Steps like this to help restrict access, alongside the provision of free parental controls and education, are key."
In 2016, an NSPCC report revealed that online pornography could impact a child's development and decision-making.
According to the same study, some 28 percent of children may have accidentally come across pornography while browsing on the internet.