There has been a more than tenfold increase in the number of people identified as victims of modern slavery and human trafficking in London, and more than 30% of all cases nationally are discovered in the capital, according to new research.

In London in 2018, the Metropolitan police recognised 2,346 people as victims of modern slavery, compared with 187 in 2013, analysis of government data by the London assembly reveals.

Of the 5,143 people referred by the Home Office for support after being identified as victims of slavery in 2017, about 1,500 were in London – almost three times the number in any other region or country in the UK.

In October, the Local Government Association reported an 807% rise in the number of child victims of modern slavery and human trafficking.

The assembly’s police and crime committee is calling for an overhaul of the way the police and the mayor’s office handle the problem, and it has written to Sadiq Khan recommending that more detectives should be assigned to the Met’s specialist crimes and vulnerabilities unit.

It is also proposing that the London modern slavery partnership board, established in 2018, should develop a London-specific modern slavery strategy to improve the capital’s response to the problem.

The committee has also called on the Home Office to change the national referral mechanism, which is the gateway to getting support.

The number of referrals has risen year on year, as has the number of pending cases, and the proportion of cases where an individual is formally recognised as a victim of trafficking and is given housing and support has been declining.

“In 2013, 47.8% of referrals received a conclusive decision; in 2018 this figure fell to 16.45%,” the committee said in a letter sent to the deputy mayor for policing and crime, Sophie Linden, on Wednesday.

Awareness of the issue of human trafficking has risen following the deaths of 39 Vietnamese people found in the back of a refrigerated lorry in Essex last October.

Theresa May introduced legislation to combat modern slavery in 2015 and described it as one of the “great human rights issues of our time”. Although most modern slavery charities welcomed the legislation, some migrants’ rights organisations have questioned whether this focus on human trafficking was simply a softer side to the government’s preoccupation with cutting net migration numbers and creating a hostile environment for illegal immigration.

There has been disappointment about a lack of funding for implementing the legislation. Figures released in December indicated that the government was failing in its attempts to tackle modern slavery, with only 42 convictions on slavery and human trafficking in 2018, down from 59 in 2017 and 69 in 2016.

Umesh Desai, the chair of the London assembly’s police and crime committee, said: “The challenge London faces with modern slavery and human trafficking is unique, and considerably greater than in any other region of the UK. It’s clear that London needs to have a more coherent strategy to tackle modern slavery and human trafficking. The rise of modern slavery cases in London over the last five years shows that action is needed now.

“That’s why we’re calling on the mayor to urgently task the London Modern Slavery Partnership Board with developing a coherent strategy for modern slavery in the capital.”

Some London councils, such as Southwark, have been working with the Met’s specialist crime unit to carry out raids on nail bars in recent months in an attempt to crack down on suspected exploitation of young Vietnamese people. In the past few months 10 children have been found working in Southwark nail bars, all of whom have been taken into care.

Southwark officials point out it has become difficult to carry out regular raids after a period of heavy local authority cuts. Victoria Mills, a Southwark councillor, said: “Local councils have been forced to make some tough decisions following a 50% cut in their government funding over the last decade. But we see the safety of the people who live, work, study and visit to be a top priority. This is why we have protected the work of our trading standards team.”