Calls for "prostitution websites" to be banned in England and Wales will be made at a House of Commons debate.
A cross-party group of MPs says the owners of such sites "directly and knowingly" profit from sex-trafficking and wants the Home Office to intervene.
The group adds that a small number of sites "dominate the marketplace" and have named two in particular: Vivastreet and Adultwork.
But sex-worker-rights campaigners say the proposal would be "a disaster".
Three organisations - the Sex Worker Advocacy and Resistance Movement (Swarm), the English Collective of Prostitutes (ECP), and the xTalk collective - are planning a demonstration outside Parliament at the time of this Wednesday's debate to protest against the suggested law change.
They describe the idea as being a "Trump-inspired" effort to kick sex workers off the internet and put them into "more exploitative and harmful situations".
The debate follows a report into sexual exploitation in England and Wales, which was published in May.
It concluded that prostitution procurement websites were "the most significant enabler of sex-trafficking in the UK".
"Websites such as Vivastreet and Adultwork are key to the typical 'business model' used by the organised crime groups and third-party exploiters who dominate the UK's off-street sex trade," the report concluded.
"Any notion that prostitution websites introduce 'safety' to the sex trade by making procurement visible is a dangerous and misleading fallacy.
"They hide sexual exploitation in plain sight."
Sarah Champion - the Labour MP for Rotherham - will lead a follow-up debate in Westminster Hall.
"Across the UK, men are paying to sexually exploit vulnerable women and girls that they have 'shopped' for online," she will say.
"We need to join the dots - between prostitution, modern slavery, trafficking and child sexual exploitation."
The MP is also calling for new rules to criminalise the payment of sex in any location, but an end to penalties for loitering and solicitation.
Both Vivastreet and Adultwork make money by charging those who post "adult" adverts rather than the people who then make use of them.
"We take the issue of exploitation extremely seriously, and we are working closely with the Home Office to help develop an industry-wide approach to identifying and preventing online trafficking," Vivastreet told the BBC.
"We are committed to eradicating any potential exploitation from our platform, and we have a wide range of measures in place to detect and remove inappropriate material. "
Adultwork could not be reached for comment.
All classifieds services are now banned from running ads relating to the sale of sexual services in the US, after the introduction of a new law.
President Trump signed the Fight Online Sex Trafficking Act (Fosta) in April.
But it now faces legal challenges of its own, with the Electronic Frontier Foundation (EFF) among others claiming that it both trespasses on free speech laws and hinders efforts to help sex-trafficking victims.
The English Collective of Prostitutes suggests the law has made it harder for US sex workers to screen their clients, and has published a blog setting out its opposition to a similar move in the UK.
"If we can't advertise online and work independently, many of us would be forced to work in other ways including on the streets where it is much more dangerous to work," it says.
"Or we will be pushed into the hands of exploitative brothel bosses.
"If well-meaning MPs want to save women from sex work then take action against zero-hour contracts, low wages and exploitative bosses in the jobs that are the alternatives to prostitution."