South Australian authorities have been criticised by traditional owners and environmental groups for issuing a permit for the culling of southern hairy-nosed wombats on the Yorke Peninsula.

The permit was issued for Aboriginal Lands Trust lands at Point Pearce, which are leased to a farmer, under laws that allow for the culling of “abundant wildlife” that is “causing damage”.

It comes a month after the Victorian government revoked a 23-year-old law that declared wombats an “unprotected” species.

The SA Department of Environment and Water refused to say what damage was specified in the request for this permit, or how many animals were intended to be culled, but Narungga traditional owners have told Guardian Australia it was a significant number.

A department spokeswoman said: “The owner of Point Pearce, Aboriginal Lands Trust (ALT), applied for and received a permit for the humane destruction of wombats.”

Under SA regulations, the department said, landholders can apply for a permit to destroy native wildlife “where those animals are damaging, or are likely to damage, the environment, crops, stock, property or environmental amenity, or are posing a safety risk or hazard to people or industry”.

The decision takes into account the species abundance, “human safety and economic considerations” and what other management methods have been “undertaken or considered”.

SA does not publish annual figures on the number and type of wildlife culled under its permit system, but figures released under freedom of information laws for 2016-2017 show that 44 permits were issued to kill 803 southern hairy-nosed wombats this year.

There’s simply no excuse for this over-the-top lethal intervention. Evan Quartermain

The Victorian government issued 252 permits to allow for the killing of 3,374 common wombats in 2017, and 268 permits for the culling of 3,830 common wombats in 2018, government data shows. Common wombats are more abundant than southern hairy-nosed wombats.

“There’s simply no excuse for this over-the-top lethal intervention, particularly considering simple solutions to prevent damage such as wombat gates are now available,” said Evan Quartermain from the Humane Society International.

“That these latest allegations of wombats being shot are on the Yorke Peninsula is particularly concerning. It’s a highly fragmented population, and Point Pearce is one of just three colonies thought to have more than 100 individuals. It’s an area of great conservation significance.”

Quartermain said legal wildlife culling, authorised by state governments, was “occurring at extremely alarming levels nationwide”.

The southern hairy-nosed wombat was nominated for threatened species listing several times under the Environment Protections and Biosecurity Conservation Act, but is not currently listed. Quartermain said the Humane Society was in the process of renominating the species, which is under threat from Sarcoptic mange and habitat loss.

The Yorke Peninsula population is the smallest of the four main wild populations, which include the Eyre Peninsula and Murraylands and the largest population of between 50,000 to 100,000 wombats on the Nullarbor plain in SA and Western Australia.

Estimates from 2014 put the population on the Yorke Peninsula at just 696 wombats spread over 25 colonies, of which Point Pearce is the largest with 135 individuals.

A native title determination confirming Narungga rights over the Yorke Peninsula, including Point Pearce, is scheduled for a federal court hearing in June.

The Point Pearce office of the Aboriginal Lands Trust told Guardian Australia on Monday it was not commenting on the issue.