The Criminal Justice and Immigration Bill, currently in the Lords, could be in force by the autumn.

It would be applied retrospectively to more than 30,000 sex offenders on the register, a Home Office spokesman said.

Failing to comply would carry up to five years’ imprisonment.

Mr Coaker said: “This is something that will be particularly useful in combating the possible grooming of children on the internet.

“We will work with the industry. It will be a matter of partnership between industry and law enforcement to make sure this law is made effective.

“What we are looking at is how to protect children.

“Law enforcement and children’s charities have said this is an issue.”

The Home Office’s online safety guidance included advice for youngsters on how to avoid placing themselves in compromising situations.

The document said: “It is important to discuss and establish boundaries with your child from an early age, about flirting online, especially when your child begins to show an interest and is beginning to use interactive services.

“Teenagers may engage in flirting or sexual exploration online, and it is important to discuss the need for boundaries in relationships even with known boyfriends and girlfriends.”

It warned youngsters not to post “sexually provocative or explicit” photographs of themselves.

Children should be urged to “think before they post”, particularly when material may involve “images from a party or of outrageous or compromising behaviour”.

The document also urged parents to learn about their children’s online activities, including which sites they use.

“Negotiate with your child to visit and view all their profiles on social networking sites,” the guidance said.

“You should not be afraid to become involved in your children’s online activities.”

Asked about potential costs to industry of barring paedophiles, chairwoman of the Home Office’s taskforce on internet child protection and head of content standards at Vodafone, Annie Mullins, said: “We haven’t had that discussion yet.

“These are complex issues. We will take the opportunity to discuss this further.”

Mr Coaker said that there was “always further scope” to expand protection, perhaps by keeping other types of sex offender off-line.

The NSPCC’s Diana Sutton said: “The proposal to monitor the access that registered sex offenders have to social networking sites recognises the integral part that these sites now play in children’s lives.

“Many sex offenders will go to extraordinary lengths to access children, and we need to ensure that safety measures in cyberspace are as stringent as they are in the wider world.”

She added: “Parents also play a crucial role in educating their children about how to surf safely online.

“They can install filtering equipment on computers used by children to protect them from seeing abusive or violent material.

“The introduction today of a kitemark scheme on these products will give parents greater confidence when buying as manufacturers will have to comply with an independent standard to gain accreditation.”

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