The move is part of a broader package of measures proposed by the U.K. government in a green paper aimed at making the internet safer.
While the green paper acknowledges that social media companies are taking action to combat bad behavior online, Downing Street believes a levy could help the situation further.
"We believe that more needs to be done and that it is right that all companies should be involved and encouraged to play their part. This is the reason we will introduce a levy, to help us combat online harms," the paper said.
"As we develop plans for the levy's delivery, we will seek to ensure that it is proportionate and does not stifle growth or innovation, particularly for smaller companies and startups. And we will make sure it does not disincentivize tech companies investing in the U.K."
The paper says that the levy will not be a tax on social media and will be voluntary. But it does not rule out underpinning the levy with legislation if needed.
Facebook did not comment directly on the levy proposal but said it is happy working with the U.K. government.
"Our priority is to make Facebook a safe place for people of all ages which is why we have spent a long time working with safety experts like the U.K. Safer Internet Centre, developing powerful tools to help people have a positive experience on Facebook. We welcome close collaboration between industry, experts and government to address this important issue," a spokesperson for the social network told CNBC by email Wednesday.
Twitter did not give a comment when contacted by CNBC but instead pointed to its current efforts to combat online abuse. The company is taking down 10 times more abusive accounts everyday compared with last year, for example.
Britain's government also proposed a new social media "code of practice" aimed at a joint approach to addressing bullying and humiliating online content. Alongside this, an annual report detailing the progress made could also be possible.
"Behavior that is unacceptable in real life is unacceptable on a computer screen. We need an approach to the internet that protects everyone without restricting growth and innovation in the digital economy," Karen Bradley, the U.K.'s digital, culture, and media minister, said in a press release.