Ministers have rejected plans to automatically block internet access to pornography on all computers, saying the move is not widely supported.
A public consultation found 35% of parents wanted an automatic bar while 15% wanted some content filtered, and an option to block other material.
But the government says internet providers should encourage parents to switch on parental controls.
Claire Perry, the MP who led the campaign, said she was "disappointed".
The NSPCC said parents' voices were not being heard.
There were more than 3,500 responses to the 10-week consultation - which included those from members of the public, academics, charities and communication firms as well as 757 from parents.
Respondents were asked to answer "yes", "no" or "maybe" to three separate questions about how internet service providers (ISP) could play a role in limiting access.
An automatic block would mean users would have to actively request that pornographic content was made available by their ISP.
Mrs Perry, the Conservative MP for Devizes in Wiltshire, led the campaign and handed over a petition to Downing Street containing more than 115,000 names.
She chaired the cross-party Independent Parliamentary Inquiry on Online Child Protection which concluded in April that government and ISPs needed to do more to keep children safe online.
She told BBC News she was "obviously disappointed that the opt-in option has been rejected" but she added: "Clearly that was not the preferred choice of the 3,500 people who responded to the consultation and we have to base policy on what's been received not what we want."
She said she was pleased internet service providers would have to actively encourage and prompt parents to switch on filters which will block adult sites to children and verify the age of the person setting up the controls.
She said the exercise had helped to obtain a "sea change in attitude" from ISPs.
The report said there was "no great appetite among parents for the introduction of default filtering of the internet by their ISP - only 35% of the parents who responded favoured that approach".
Some 13% said they favoured "a system where you are automatically asked some questions about what you want your children to be able to access".
And 15% answered "yes" to a system that combined the previous two approaches where some harmful content, such as pornography, was automatically blocked but parents were also asked about what other content their children could access.
The NSPCC said the figures showed that half of the parents who took part in the consultation wanted some sort of automatic block on online pornography.
But the report said an automatic ban - or "opt-in" - approach could lead parents into a "false sense of security" because it could not filter "all potentially harmful content".
It also did not "deal with harms such as bullying, personal abuse, grooming or sexual exploitation which arise from the behaviour of other internet users".
It added: "There is also a risk from 'over-blocking' - preventing access to websites which provide helpful information on sexual health or sexual identity, issues which young people may want information on but find difficult to talk to their parents about."
About 70% of the 78 voluntary and community sector organisations that responded answered "yes" to an automatic block while a strong majority of respondents from all other groups answered "no".
While a large majority of the 77 information and communication businesses questioned were against all forms of control, they gave most support (about 18%) to the second approach, in which parents decide what they want their children to access on the internet.
The report found that, taking respondents as a whole, the majority were against all forms of control with more than 80% answering no to each of the three questions.
It praised the the four main ISPs - BT, TalkTalk, Virgin Media and Sky - for signing up to a code of practice, offering customers a choice of whether to apply filters, but said providers should go further and actively encourage parents to turn them on.
The NSPCC said that while the government's response was "a step in the right direction in making the internet safer for children" it was "disappointing" it had not gone further.
"The best option to protect children is for adult content to be automatically blocked by internet service providers," head of corporate affairs Alan Wardle said.
"Hardcore pornographic videos are just a few clicks away and a quarter of children have been sent unsolicited sexual material online."
He said it was vital new measures were rolled out to new and existing customers "quickly".
Nick Pickles, director of Big Brother Watch, which is opposed to default filtering, said: "This is a positive step that strikes the right balance between child safety and parental responsibility without infringing on civil liberties and freedom of speech.
"The policy recognises it is parents, not government, who are responsible for controlling what their children see online and rightly avoids any kind of state-mandated blocking of legal content."