The party wants the government to bring forward legislation that would include financial and criminal penalties for companies that fail to act against such content.
Labour has claimed dedicated anti-vaccination groups with, hundreds of thousands of members on social media, are “churning out disinformation” on the issue.
Shadow culture secretary Jo Stevens and shadow health secretary Jonathan Ashworth have written to Culture Secretary Oliver Dowden insisting that the “spread of disinformation online presents a real and present danger” to vaccination efforts.
Ms Stevens said: “The government has a pitiful track record on taking action against online platforms that are facilitating the spread of disinformation.
“It has been clear for years that this is a widespread and growing problem and the government knows, because Labour has been warning them for some time, that it poses a real threat to the take up of the vaccine.
South Australia has recorded four new cases of coronavirus, including an 80-year-old woman who is being considered as a new community transmission case.
SA Chief Public Health Officer Nicola Spurrier said the woman was tested in Lyell McEwin Hospital yesterday morning and remains in hospital in a stable condition.
“In the last couple of minutes before coming to the press conference I’ve also received two positive results from family members of this case,” she said.
“Of the two family members there’s a female in her 50s and a male in his 60s, and the important thing to note is that one of those people works in one of our medi-hotels.”
“So that’s very early information, we still will be doing genomic testing but obviously this is where we are considering the source to be.”
Professor Spurrier said SA Health is in the process of contacting people who may have been in contact with the 80-year-old woman at the Lyell McEwin Hospital.