Eurostar says it saw a fall in passenger numbers in the first three months of this year, down by three percent overall to 2.2 million.
Sales declined by six percent to 201 million pounds (260 million euros) between January and March compared to the same quarter last year
But Eurostar believes the Euro 2016 football tournament starting in France next month will help drive a recovery.
It has seen a “surge” in bookings in recent weeks linked to the event and expects 500,000 Britons to travel to the matches.
The cross-channel high-speed rail service blamed the terror attacks in Paris and Brussels for the fall off saying “travellers remain cautious” with a particular reduction in passengers from the United States and south-east Asia.
Eurostar sales hit by terrorist attacks: Company saw demand fall particularly from US and Asian travellers https://t.co/z27k4ECp93— TTG (@TTGMedia) May 20, 2016
The company said that from past experience it should take around 12 months for numbers to return to previous levels after those attacks.