The government needs to find an extra £2.7bn to tackle the growth in serious and organised crime that is causing “staggering” damage to the United Kingdom, according to the director general of the National Crime Agency.

Lynne Owens is due to make the direct challenge to ministers on Tuesday as she launches the agency’s annual national strategic assessment mapping out dangers from cyber crime, child sexual exploitation, drugs and other serious and organised crime.

The NCA, which was set up by the Conservative government in 2013, says there are at least 181,000 people linked to serious and organised crime in the UK – twice the size of the British army.

There are 37,000 active organised criminals and 144,000 people in the UK “registered on the most harmful child sex abuse … dark web sites,” the agency says, insisting its estimates are conservative and not scare tactics.

Owens is due to tell the launch event in central London: “Serious and organised crime in the UK is chronic and corrosive; its scale is truly staggering. It kills more people every year than terrorism, war and natural disasters combined. Serious and organised crime affects more UK citizens, more frequently than any other national security threat.

The agency estimates serious and organised crime costs the UK £37bn a year, equivalent to £2,000 for each family.

Owens is calling for an extra £650m to be given to the NCA and for £2.1bn to fund agencies such as the Border Force and go to police efforts fighting serious and organised crime.

She will say: “We need significant further investment to keep pace with the growing scale and complexity. Some will say we cannot afford to provide more investment, but I say we cannot afford not to.”

The sum asked for is the equivalent to a half penny on income tax, but comes as other demands are being made to provide extra funding for the police and other key public services.

A full spending review is supposed to happen within months but there is increasing expectation the tumult caused by Brexit may mean it is postponed until after the UK has made a decision on its future in the EU.

Owens will say: “The choice is stark. Failing to invest will result in the gradual erosion of our capabilities and our ability to protect the public.”

The assessment warns that Brexit could “impact the prevalence of bribery and corruption over the next five years, as UK companies potentially come into greater contact with corrupt markets”.

Referrals for key crime types are increasing, with some of the rise accounted for by better reporting and increased awareness. Modern slavery referrals are up 80% since 2016, and about 2,000 county lines drug routes are in use compared with 720 a year earlier.

The NCA says some organised crime groups are made up purely of children and young people “adopting businesslike operating models rather than relying on identity or postcode”.

The agency warns of corruption among public officials, especially at the border, and among professionals such as solicitors and accountants who do the bidding of those involved in serious and organised crime.

A Home Office spokesperson did not directly address the call for more money, but said: “We continue to invest in the right capabilities and tools in law enforcement, across government and in partnership with the private sector.”

John Apter, who chairs the Police Federation, said government cuts to policing, of around 19%, had helped serious and organised crime flourish. “This is the reality of years of austerity where we have seen the number of police officers reduced by almost 22,000 as the number of organised criminals has increased; the NCA is therefore right to say considerable investment is needed,” he said.

Diane Abbott, the shadow home secretary, accused the government of being in denial, adding: “If the Tories were genuine about tackling serious and organised crime, they would provide all the funding that’s needed.”