As many as 13,000 people in Britain are victims of slavery, about four times the number previously thought, analysis for the government has found.

The figure for 2013 marks the first time the government has made an official estimate of the scale of modern slavery in the UK, and includes women forced into prostitution, domestic staff, and workers in fields, factories and fishing.

The National Crime Agency (NCA)’s human trafficking centre had previously put the number at 2,744.

Launching the government’s strategy to eradicate modern slavery, the home secretary, Theresa May, said the scale of abuse was shocking.

“The first step to eradicating the scourge of modern slavery is acknowledging and confronting its existence,” she said. “The estimated scale of the problem in modern Britain is shocking and these new figures starkly reinforce the case for urgent action.”

The data was collated from sources including the police, the UK Border Force, charities and the Gangmasters Licensing Authority. The Home Office described the estimate as a “dark figure” that may not have come to the NCA’s attention.

Professor Bernard Silverman, the chief scientific adviser to the Home Office, said the new statistical analysis aimed to calculate the number of “hidden” victims who are not reported to the authorities.

“Modern slavery is very often deeply hidden and so it is a great challenge to assess its scale,” he said. “The data collected is inevitably incomplete and, in addition, has to be very carefully handled because of its sensitivity.”

The modern slavery minister, Karen Bradley, told the BBC the issue was a hidden crime. “What we have to do today is not make people acknowledge it’s wrong - everybody knows it’s wrong - but we have to find it,” she said.

“It’s going on in streets, in towns, in villages across Britain and we need to help people find the signs of it so we can find those victims and importantly then find the perpetrators.”

The modern slavery bill going through parliament will provide courts in England and Wales with powers to protect victims of human trafficking. Scotland and Northern Ireland are planning similar measures.

May said: “Working with a wide range of partners, we must step up the fight against modern slavery in this country, and internationally, to put an end to the misery suffered by innocent people around the world.”

The Home Office said the UK Border Force would introduce specialist trafficking teams at major ports and airports to identify potential victims, and the legal framework would be strengthened for confiscating the proceeds of crime.

But Aidan McQuade, the director of the Anti-Slavery International charity, questioned whether the government’s strategy went far enough.

He told BBC Radio 4’s Today programme: “If you leave an employment relationship, even if you’re suffering from any sort of exploitation up to and including forced labour, even if you’re suffering from all sorts of physical and sexual violence, you’ll be deported.

“So that [puts] enormous power in the hands of unscrupulous employers. And frankly, the protections which the government has put in place are not worth the paper they’re written on in order to prevent this sort of exploitation once they’ve given employers that sort of power.”

Many victims are foreign nationals from countries such as Romania, Poland, Albania and Nigeria, but vulnerable British adults and children are also systematically preyed upon by traffickers and slave drivers. The NCA estimates that the UK was the third most common country of origin for slavery victims.

In November last year three “highly traumatised” women were rescued from a house in south London where they appear to have been held captive for three decades, Scotland Yard said. One of the women contacted Aneeta Prem, the founder of the Freedom Charity, after seeing her on TV.

A couple, both in their late 60s, remain on bail after being arrested on suspicion of being involved in forced labour and domestic servitude.

Prem said the south London case had raised awareness of the problem, and that the charity had been receiving more calls.

One of the biggest barriers to freeing victims was the repercussions that family members living in other countries could face, she said. That meant action had to be coordinated with authorities overseas and could take time to arrange.

People needed to be more aware of the problem, she said, and urged anyone who had concerns that “something doesn’t seem right” to contact Freedom.