Sea Life Manchester say UK aquariums are at capacity and terrapin owners are taking to putting the reptiles down the toilet to avoid being caught illegally releasing them into the wild.
It adds that recent EU invasive alien species regulations now prohibit aquariums from taking in pet terrapins or moving terrapin stock to other aquariums.
As a result, it says, public ponds, canals and lakes are home to large numbers of the terrapins that have survived the journey through Britain's sewerage plants.
The centre's lead curator Alan Kwan said: "People wrongly assume that terrapins are going to be easy to care for. What they don't realise is they grow from a hand-sized 3cm in length to 30cm, the size of a large dinner plate, and live between 30 and 50 years.
"Global warming and the resulting rise in temperatures across British waterways is leading to abandoned terrapins breeding and growing in population.
"Native to Florida, this alien predatory reptile is having a damaging effect on British pondlife and waterfowl with fish, frog, frogspawn and ducklings falling prey."
Sea Life Manchester, based at the Trafford Centre, want people to think twice before buying a terrapin as a family pet.
The centre has named one of its 18 rehomed unwanted pet terrapins as Loo to highlight the problem.