For years, they were the scourge of seabirds seeking to nest on Lundy.

But since rats were expunged from the island off the coast of Devon 15 years ago, the seabird population has trebled to 21,000 birds.

Puffins have increased from 13 birds in 2001 to 375, while the population of Manx shearwaters has risen from 297 pairs to 5,504, according to a study led by the RSPB.

Black and brown rats, which arrived on Lundy as stowaways on ships, preyed upon the eggs and chicks of ground-nesting seabirds, particularly the burrow-nesting puffins and shearwaters. Between 2002 and 2004, the non-native rats were eradicated – a project opposed by some animal rights groups, who argued that conservationists were favouring tourist-friendly birds over the rats.

Since Lundy was declared rat-free in 2006, its seabird populations have bounced back, as they have on other small islands when invasive predators introduced by humans have been removed.

There were more than 3,500 pairs of puffins in 1939 but fewer than 10 pairs in 2000, with fewer sand eels in the surrounding seas as well as the rats contributing to their decline. While 75% of the global population of Manx shearwaters breed on British islands, Lundy’s population by the turn of the century was far lower than its potential, and much less than on nearby islands such as Skokholm, where 350,000 pairs nest.

Dean Jones, the warden on Lundy, which is managed by the Landmark Trust, said: “It is exciting to see this level of recovery in Manx shearwaters, one of our most important seabirds. In spring the island comes alive at night with the sound of these amazing birds. The increases in puffins, guillemots and razorbills is also very encouraging for the future of seabirds on Lundy and we are maintaining our vigilance to ensure rats cannot return to the island.”

Helen Booker, senior conservation officer for RSPB in south-west England said: “This study clearly shows how quickly and positively seabirds respond to the removal of non-native predators. Of course, we had anticipated major population increases when the project was launched, but the scale of this recovery has far exceeded our expectations.”

A recent study found that nearly 10% of the world’s bird, mammal, amphibian and reptile species currently on the brink of extinction could be saved by culling invasive mammals such as cats and rats on 169 islands.

On British islands, rat eradication programmes have been successfully completed on the Shiants in the Hebrides and on St Agnes and Gugh in the Isles of Scilly, with seabird populations subsequently bouncing back.

But rat eradication programmes have been controversial with some animal rights activists, who have argued that the black rat, although not native to Britain, is one of the country’s most endangered mammals.