The trust said some of the creatures have been in the UK for so long, they are thought of as indigenous.
A number of non-native mammal species are damaging the UK countryside by eating crops and threatening wildlife, a conservation charity has warned.
A report by the People's Trust for Endangered Species identified 14 problem species including rats, American mink and muntjac deer.
It said it was important to stop the extinction of native species.
American minks prey on water voles while grey squirrels, which were introduced to the UK in the 19th century carry the deadly squirrelpox virus and outcompete the native red squirrel when it comes to hunting for food and habitats.
According to the report, two of the UK's fastest declining native species the red squirrel and the water vole - which has declined by 90% - are under threat by mammals introduced by humans in the last two centuries.
The trust also warned the red-necked wallaby is capable of damaging capercaillie birds on Loch Lomond island, while muntjac deer congregating in high numbers are also accused of being a threat to wildlife.
According to the British Deer Society, muntjac were brought from China to a park in Bedfordshire in the early 20th century.
They spread across the country after they escaped, or were deliberately released, from the park.
The trust said the species can have a negative impact on UK wildlife, landscape and agriculture. This range of problems include carrying disease, breeding with species to produce hybrids and altering the landscape and damaging crops.
People's Trust chief executive Jill Nelson said: "Our campaign to conserve Britain's native mammals is rooted in finding more about each animal's behaviour in response to the various threats they face and translating that knowledge into practical conservation action."
She said the way with how the UK dealt with the problem was a "vital component in preventing their extinction".
The report also warned that global trade and a changing climate could lead to the invasion of more alien species.
Other species to have made the list include house mice and rabbits.
But the report, researched by professor David Macdonald and doctor Dawn Burnham from the University of Oxford Wildlife Conservation Research Unit acknowledged, that while rabbits are mainly seen as a pest, they can also have a positive conservation effect in particular areas where they graze.
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