The consultation reveals that 57 per cent of the 757 parents who responded to the consultation were in favour of stricter controls, including 47 per cent who wanted an opt-in system.
However, in total, just one in six of the 3,509 respondents - most of whom were not parents - supported the full opt-in solution.
Two-thirds of the respondents were from just one pressure group called the 'Open Rights Group', which is against default filters to block net porn.
Children's charities will be concerned that the consultation has been swamped by those opposed to stricter controls.
Labour's media spokesman Helen Goodman, who wants to see an opt-in system, criticised the Department for Education for still not having published the results of the consultation two months after it ended.
Two meetings of the UK Council for Child Internet Safety (UKCCIS) to discuss the consultation responses have been cancelled, leading to accusations that ministers are dragging their feet.
'It is shocking that despite the findings of the consultation being known, and the urgency of this issue, the Government has yet to respond to the consultation,' said Miss Goodman.
'In particular, the finding that 41 per cent of parents say their children have been exposed to pornography shows why the Government should take urgent action.'
The consultation asked parents whether their children had been exposed to a range of online dangers. Highest on the list is pornography, with 41 per cent of parents said their offspring had seen it.
The second-largest danger was sexually explicit messages, with 31 per cent of parents saying their children had received so-called 'sexts'. Some 27 per cent of parents said their children had been exposed to violence, 26 per cent to gambling and 23 per cent on bullying.
Another 22 per cent believe their children have been abused by text, while a similar proportion have been exposed to drink or drugs.
Other online dangers reported by parents include websites promoting self-harm (10 per cent), anorexia (9 per cent), suicide (8 per cent) and radicalisation (8 per cent). Some 9 per cent of parents said that their children had been exposed to the risk of sexual grooming by men.
The document concluded: 'Children's online safety is the responsibility of parents or a shared responsibility between parents and businesses.
'The majority of respondents were opposed to all of the three options for parental controls consulted on.
'Parents are concerned about potentially harmful content such as pornography and violence, and behavioural issues, such as sexting and bullying.
'Increasing the level of education and awareness among parents will make it easier for them to use parental controls, and limit exposure to risks online.'
The document advised UKCCIS to support an industry-designed scheme under which customers choose the option that is 'right for their family and circumstances'.
'Providers will take measures to check that the person setting up the parental controls is over the age of 18,' it said.
- Daily Mail