Theresa May has urged fellow EU leaders to join the UK in a crackdown on people smugglers who are using social media sites to pose as “travel agents” for desperate migrants.

The prime minister said concerted action is needed across Europe because of the international nature of the online problem, as she pressed for action to stop traffickers using sites such as Facebook to reach victims.

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She told the leaders at a summit in Salzburg on Wednesday that the UK would continue to be fully committed to working with them on the “generational challenge” of migration after Brexit.

Police and security officials believe the traffickers’ adverts are presented as reassuring and create an illusion that this is normal travel – rather than the reality of being packed on to a dangerous rubber rib or a small boat without safety jackets. One page even offered discounts for children, a UK source said.

In the last year, UK law enforcement agencies have referred 539 social media pages advertising people smuggling services for closure by Europol.

But at a working dinner with EU counterparts, May explained online platforms had “no respect for borders” and unless the countries acted together traffickers would simply “exploit our weakest link”.

May offered to share expertise and put the UK in the lead of a joint effort to work with social media platforms to prevent traffickers using their websites.

She also suggested that the approach used to tackle extremist propaganda online should be employed to target the gangs behind people trafficking. This includes building on existing work with social media firms and Europol’s Internet Referral Unit to take down the exploitative adverts straight away, and seeking to change the behaviour of migrants whose lives could be in danger.

The European council president, Donald Tusk, urged leaders at the gathering to stop the “blame game” about the migration crisis and hit out at populist politicians seeking to exploit the issue.

“Despite the aggressive rhetoric, things are moving in the right direction,” he said, with the number of irregular migrants down from almost two million in 2015 to fewer than 100,000 this year. So, instead of taking political advantage of the situation, we should focus on what works and just get on with it. We can no longer be divided into those who want to solve the problem of illegal migrant flows, and those who want to use it for political gain.”