Invasive species such as Japanese knotweed, signal crayfish and New Zealand flatworms must be subject to stronger safeguards after Brexit, a group of conservation charities has urged, or the cost of dealing with them may spiral.

They fear that future increased international trade outside EU rules could threaten further invasions, while the status of safeguards under potential trade deals could be put in doubt.

The cost of managing invasive species, and dealing with the consequences of their spread, is already likely to be more than £2bn a year by conservative estimates, according to Wildlife and Countryside Link, a consortium of 12 NGOs calling for government assurances. They said that in the past three years alone, three of the highest-risk invasive species – the Quagga mussel, the Asian shore crab and the brush-clawed shore crab – have made their presence felt.

Non-native species arrive in the UK through imports of ornamental or aquatic plants, on ship hulls or in their ballast water, or inside the packaging of plants and food – even lurking within wood and fruit. Once they take hold, they threaten native species, spread disease and parasites, and a lack of natural halts or predators in the UK can allow them to flourish.

Japanese knotweed is resistant to even strong pesticides, and its easy adaptation to the UK climate means it grows swiftly and can threaten subsidence to building foundations where it takes hold; it is calculated by the charities to have caused about £200m in damage last year. The signal crayfish has devastated the population of native white crayfish at a cost of at least £2m a year, while New Zealand flatworms have caused the population of native earthworms to plunge. In Scotland, the damage was estimated at £23m, and £34m in Northern Ireland.

Facebook Twitter Pinterest New Zealand flatworms have caused plunges in the populations of native earthworms. Photograph: GB Non-native Species Secretariat

The charities said the opening up of new trade routes outside EU rules meant “the potential for new opportunities for species to travel across these pathways and establish themselves in the UK”. At present, EU rules prevent the import of some plants and animals, and provide for checks on containers and regulations on transport such as shipping.

Elaine King, director of Wildlife and Countryside Link, said: “Opening our doors to new trade post-Brexit also opens the door to new nature invaders. It is essential the government put the right measures in place to stop harmful species putting down roots and taking a bite out of our economy.”

Hannah Freeman, senior government affairs officer at the Wildfowl and Wetland Trust, part of the coalition, added: “Robust co-ordination, strong prevention and enforcement, and firm legal underpinning are all essential to turn away harmful nature invaders from our borders.”

The charities also called for new resources to be spent on controlling non-native invasive species, on which the government spent about £1m in 2016-17 in England. The last major work on the cost of invasive species comes from 2010, when it was estimated at £1.7bn a year, and Wildlife and Countryside Link have updated this with inflation calculations from the Bank of England. This week, activities are taking place around the country to raise awareness of invasive species and help to control their spread.