The small insect - Nezara viridula or southern green stinkbug - is native to far warmer climes in North America, South America and Africa.
It has never before been known to breed in chilly Britain, said Max Barclay, curator of beetles at London's Natural History Museum.
"A book on British bugs written in 1959 noted that the climate was too cold for stinkbugs to survive," Barclay said on Friday.
"But we have now found three breeding colonies of them here which is clear proof that the climate has changed in the last 50 years, and particularly in the last three or four," he added.
The stinkbug, so named because of the stench it produces if threatened, is a plant killer that can ravage food crops.
But it is also considered a delicacy to eat in Mexico.