Twitter and Instagram have been criticised by an MP for failing to remove posts advertising Xanax.
There is evidence the anti-anxiety medication is increasingly being used recreationally by young people, some of whom have needed hospital treatment.
Xanax's manufacturer Pfizer said anyone buying it on social media will be buying fakes.
Twitter said the adverts were organic content created by users rather than being official advertising.
Bambos Charalambous, the Labour MP for Enfield Southgate in London, raised concerns about the drug in parliament. He said: "I'm very concerned that accounts are still up after being reported.
"I think social media companies need to take greater and swifter action to stop these dealers from selling Xanax online."
In January, Mr Charalambous told the Commons about the 14-year-old daughter of a constituent who ended up in temporary foster care and was expelled from school because of her use of Xanax.
The BBC found that while Facebook was quick to take down posts advertising and promoting Xanax, Twitter failed to remove any of 16 posts and pages reported to it as part of this investigation until contacted for comment.
These were posts promoting the drug created by Twitter's users, rather than being official advertising.
Instagram took seven of 10 posts reported to it down within two weeks, but one post remained active when the BBC approached it for comment.
John, 17, says he takes Xanax recreationally as it's an easily accessible drug and only costs about £10 for five pills - although he fully expects these tablets are fake as it's difficult to get hold of the genuine article in the UK.
"It kind of takes away your care for a lot of things, a lot of things going around your head it just takes it that away."
The teenager says he first took the drug with friends, and later to help him sleep, but it made him forgetful, and made others do things they wouldn't normally do.
"It kind of got out of hand, I took too much Xanax, forgot how much I took. The next thing I knew I had to go to A&E. I blacked out, I don't remember anything, really, and I couldn't really walk properly."
He says one friend has had a seizure as a result of Xanax use.
Xanax is the trade name of the drug alprazolam, which is widely prescribed in the US to treat anxiety and can be obtained on private prescription in the UK.
Neville Broad, counterfeit laboratory manager at Pfizer's research base in Sandwich, Kent, said the lab was finding pesticides, insecticides, rat poison and lead paint in the tablets it tested.
"The worst-case scenario is death," he warned, adding that some of the fakes "were indistinguishable to real products to the untrained eye".
A member of the company's global security team warned that the use of fake Xanax was increasing.
"What we are seeing is a fast-developing market controlled by criminals and organised crime groups," he said.
"We are seeing China as a market for active ingredients, and increasingly we are seeing the raw materials being shipped into the UK."
He said criminals were buying pill presses from China, with the production of fake medicines such as Xanax taking place in Britain.
"We do see it being produced in London, and pass on intelligence and evidence to the police where we have it," he said.
"It is low risk and high profit for the criminals concerned."
He also said that anyone who bought Xanax online, without a prescription, would almost certainly be purchasing counterfeit drugs.
"Pfizer do not produce a red Xanax. Pfizer don't ship it out in little plastic bags," he said.
"We are now seeing Xanax being advertised by dealers as a liquid, powder, sweets, vape or mouthwash."
A spokesperson from the Met Police said: "Counterfeit medicines are extremely dangerous and when individuals consume them they can never be certain of what substances they contain.
"Where we receive any information to suggest that such offences are being carried out in London, we will investigate."
A Twitter spokesperson said: "These accounts are not advertising on the platform - this content is organic. Our dedicated teams will review the reports and take action where appropriate.
"Illegal behaviour can be reported by law enforcement to our legal teams who are on call 24/7 365 days a year."
If you have more information about this or other stories you would like BBC London to investigate, you can email in confidence: firstname.lastname@example.org