The longer a dog lives with the disease untreated, the greater the risk it will be transferred to a fruitfly and then on to another dog, he said.
The risk of infection is compounded by the fact that not all animals display symptoms.
As well as dogs, T callipaeda is capable of infecting cats and wild creatures such as foxes.
The Pet Travel Scheme (PETS), governing the movement of animals from European Union countries, was introduced in 2001 and updated in 2014 to include a new style of passport and additional security measures.
Dogs travelling back to the UK are required to be treated for tapeworm between 24 hours and five days before they return, and their rabies vaccinations must be up to date.
In July 2016 it was reported that a collie cross had contracted T callipaeda after returning from Romania.
Writing in the BMJ, researchers also report that a fox hair terrier returning from northern Italy and a West Highland white terrier returning from a month in France also caught the disease.
Mr Graham-Brown, a doctoral student, said the PETS safeguards were “clearly not sufficient”.
“It’s a good time to have a discussion about whether they are strong enough for this disease and other diseases,” he said.
T callipaeda is currently endemic in Italy, France, Switzerland, Germany, Spain, Portugal, Bosnia and Herzegovina, Croatia, Romania, Bulgaria, Hungary and Greece.
The BMJ paper warns that the infection of wild animals with the disease could form a “reservoir” of the pathogen, making it far harder to control thereafter.
It advises any owners concerned their dog may have been infected to seek immediate help from a vet.