The government has rejected Labour calls for specially-trained teachers to be brought in to educate children about the dangers of internet pornography.
Children as young as five are being taught about "e-safety" as part of a push to limit access to sexual images.
Labour peer Lady Hughes said such a "difficult" issue could not be taught properly in computer science classes.
But Education Minister Lord Nash said the government "trusted" teachers to deliver the message.
And he rejected the Labour peer's call for personal and social health education to be made part of the national curriculum.
On Tuesday, the government announced it had reached a deal with the five biggest internet service providers in the UK to encourage users to switch on filters blocking access to pornographic websites if there are children in the household.
The ISPs also agreed to increase funding for the Internet Watch Foundation so that it can start removing images of abuse from the internet.
But they have reportedly rejected calls by David Cameron's adviser on preventing the sexualisation of childhood, Claire Perry, to impose parental filters for adult content as a default setting.
Former children's television presenter Lady Benjamin called on the government to take action on the issue in the House of Lords.
She told peers: "Unfortunately there are many vulnerable children without parents or who have uninterested parents so no amount of awareness or education will help these kids. Many are already re-enacting pornographic behaviour with other children, as highlighted by the NSPCC.
She said the government should "block porn and all adult material by default as part of the solution to protect all children before they end up in a moral wasteland".
Tory peer Lord Nash, responding for the government, said: "We have asked the ISPs to actively encourage people to switch on parental controls if children are in the household, whether they are new or existing customers and the ISPs regularly contact existing customers through emails and on their bills.
"We also want the ISPs to put in measures to check the person setting up the parental controls is over the age of 18.
"Public wifi providers are now filtering pornography in public places and there is work underway with device manufacturers and retailers to encourage greater availability of parental controls."
The peer, a former venture capitalist and education charity boss, said it was "quite clear that too many members of our modern generation are subjected to unacceptable sexual images and they should be taught about the importance of relationships".
He said the government wanted the industry to "develop robust age verification systems to prevent children and younger people being able to access these images".
But it would be "difficult" to apply age verification to all pornographic websites as most were hosted outside of the UK, he said.
ISPs were also "bringing in 'closed-loop' emails so that when the filters are changed in the home an email is sent to the account holder and therefore the adult."
Lady Lane Fox, founder of online travel agent lastminute.com, said schools had an important role to play in educating children about internet safety
Lady Hughes, for Labour, also stressed the importance of education but said "it requires teachers trained in addressing these difficult personal and social issues and that won't happen in a computing class".
Lord Nash said primary and secondary schoolchildren were now being taught about "e-safety" - but he rejected Lady Hughes' call for specialist teachers, accusing Labour of not trusting existing teachers to "deliver the pastoral care that children need".
In May, the the National Association of Head Teachers called for children to be educated in web safety as soon as they started using the internet.
An independent survey of 1,009 parents for the NAHT suggested 83% felt pupils should learn about the dangers of pornography in sex education lessons.
The Children's Commissioner for England has warned children's attitudes to sex and relationships were being damaged after being raised on a "diet of pornography".