According to the charity, an average year before Brexit saw approximately 1,400 transfers between the UK and other EU countries.
In 2021, this dwindled to just 56, while this year has so far seen 84.
Swapping animals for breeding programmes is essential in order to keep the gene pool as broad as possible, Biaza argues.
Nicky Needham, the organisation’s senior manager for animal care and conservation, said: “Animal transfers between zoos and aquariums are carefully planned to maintain a healthy genetic population”.
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She added: “These are safety net populations for threatened species.”
Ms Needham said there are more than 400 European Endangered Species Programmes (EEPs), with UK zoos and aquaria involved in coordinating about 25 percent of them.
But the number of transfers has dropped significantly, the Biaza manager told the Guardian, pointing at Brexit as a point of inflexion.
Backing Ms Needham’s view, Zak Showell, Shaldon Wildlife Trust’s chief executive, told the outlet: “Prior to Brexit this would not have been a problem.
“It would have taken a month or two to organise for the animal to get collected by a specialist transport company.”
Many of the SPS checks need to be carried out at border control posts, which are usually set up by private enterprises. A lack of such posts at French ports — there are none — means there is essentially a ban on the import of any large animal.
As some EU airports count with control points, the few animals that have been transferred successfully to European zoos after December 31, 2020 have travelled by plane.
A Defra spokesperson said: “This shows the real harm the bureaucratic approach the EU has chosen to take on animal and plant health.
“We’re ready to continue to negotiate on this where sensible pragmatic compromises can lead to improvements for everyone.”
They added: “Meanwhile we are working closely with the Animal and Plant Health Agency and the British and Irish Association of Zoos and Aquariums to identify priority exports where there are welfare concerns or implications to breeding programs.
“All of the requests for export health certificates for the exports of zoo animals have been successfully fast-tracked.”
Conservationists’ concerns came as UK-EU post-Brexit relations hang by a thread over a number of unresolved issues which the future prime minister will be faced to deal with once handed the keys to No10.
Conservative leadership frontrunner Liz Truss last month vowed to scrap all remaining EU laws by the end of 2023 if she wins the Tory contest.