The plans follow the suicide of a London schoolgirl, Tallulah Wilson, who had spent months accessing blogs about self-harm and suicide on Tumblr beforehand.
Her mother, Sarah Wilson, described Tallulah having entered "a world where the lines between fantasy and reality became blurred", and called on companies to "withdraw their advertising from those sites who continue to host inappropriate self-harming and suicide-promoting blogs to stop this poison spreading".
Miller is expected to echo Wilson's call, and demand that social networks be more proactive about tackling content which could be harmful to younger users.
The government is reportedly feeling emboldened having won the fight over filters on the internet, and is now aiming to do the same thing for social media sites.
Tumblr already bans blogs which encourage self-harm, but, in common with most other social networks, only acts when infringing accounts are brought to its attention.
UK law currently distinguishes between publishers, who pre-emptively edit content and are held liable for everything they host, and platforms, which are exempt from liability until they are given notice. Without such a distinction, networks argue that they would be forced to close.
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image: © Howard Lake