They arrived on our shores in just a few numbers with no fanfare.

But years later, they have become a common sight across the countryside and have provided unwanted competition to our native species.

Many were brought into the country by humans and have been over here so long that we have forgotten that they came from overseas in the first place.

But for the first time, the cost of our alien invaders has been calculated, showing that Great Britain spends more than �1.7bn a year on managing invasive non-native species.

The new report by the CABI for Defra and the Scottish and Welsh governments highlights the top 20 most costly foreign fauna and flora to the British economy – many of which can be found in our region.

The environmental organisation calculated the huge cost of lost crops, decimated forests, loss of tourism, and damaged roads and rail infrastructure, which have been caused by a handful of thriving non-native species.

The total cost also includes the money spent on trying to control rapidly expanding populations, which pose a threat to Britain's biodiversity and native species.

In England, the estimated loss to the economy was �1.3bn, with the rabbit – once bred for its meat and fur at warrens in the Brecks centuries ago – causing the most damage to the agriculture and horticulture industries at �263m a year.

Other non-native offenders include Japanese Knotweed (�179m), which causes structural damage to roads, rail lines, and homes, the brown rat (�62m), non-native deer (�35m), and grey squirrel (�14m).

The study also warns that the costs will continue to rise and recommends prevention and early action to stem the boom of invasive species.

Conservationists in Norfolk welcomed the report, but added that the potential cost of losing native species was not calculated in the figures.

Mike Sutton-Croft, co-ordinator of the Norfolk Non Native Species Initiative, said the majority of non-native species posed little harm. However, a select few are causing headaches for authorities.

'There is a big risk from aquatic non-native species in Norfolk. We have got off lightly with Japanese Knotweed and we do not have as much as other places. As Norfolk is isolated, we have missed quite a few. We do have a lot of problems with Signal Crayfish and mink and goose populations are growing pretty quick.'

'It [the CABI report] has brought it to people's attention that those alien invasive species have a significant economic impact and highlights that it is better to be proactive before they become a problem,' he said.

Mr Sutton-Croft is currently working an a �20,000 project to rid floating pennywort from the River Waveney on the Norfolk-Suffolk border, which can form a 2ft mat on the surface and grow 20cms a day.

The CABI highlights the work to cull the coypu from the waterways of East Anglia in the 1980s, which cost �2.5m, as a good example of avoiding even greater costs in the long-term. The �73,000 spent on eradicating water primrose is also a drop in the ocean compared to the estimated �242m to the economy if no action had been taken.

However, the study also suggests that it would cost Britain �1.5bn to get rid of Japanese Knotweed completely and �850m to eradicate the grey squirrel.

Brian Finnerty, spokesman for the NFU East Anglia, said invasive non-native species were a big issue in the agricultural industry, with farmers and growers on the front line mostly picking up the tab.

'Everyone has a part to play in controlling invasive species and we would like to see greater public awareness so that people know what to look out for and what they should do. The public have a key role to play in recognising their responsibility when disposing of plants and animals into the wild.'

'We would like to see further research into future pests and diseases which may arise with climate change,' he said.

Richard Benyon, minister for the natural environment at Defra, added: 'It becomes increasingly difficult and costly to control invasive non-native species as they become more established.

'Taking early action may seem expensive, but this report shows that it is the most effective approach, saving money in the long run and helping our native wildlife to thrive.'