The Department of Conservation recently declared them "public enemy number one" for birds and the Government has poured millions of dollars into 1080 poison drops and research to control them.
However, new New Zealand-led research published in the journal Molecular Ecology has found that when the stoat population in Britain crashed, their expat relatives in this country conserved a reservoir of genetic diversity.
"History has demonstrated that even well-intentioned introductions of species to non-native habitats are almost always a bad idea," said Professor Robbie McDonald, of the University of Exeter.
"That said, as a result of a series of misguided introductions, we have accidentally created an 'invasive ark' for genetic diversity in New Zealand.
"It would be a fascinating long-term experiment to return native genotypes back to Britain from New Zealand and see whether it re-established among its ancestors."
Fellow author Dr Andrew Veale, formerly at the University of Auckland, said that while invasive, non-native species were a global cause of biodiversity loss, "our results show that sometimes these introduced populations may paradoxically conserve diversity lost from their native range - and potentially this diversity may be worth protecting".
Auckland University co-author Professor Mick Clout said the discovery that they had a higher genetic diversity here than back in their homeland was "intriguing". But that did not mean New Zealand stoats had any value or were worth protecting.
"If the Brits wanted to have them, then fine, but we are not going to compromise our control because of genetic diversity."