Rail services to Europe are getting rapidly booked up by airline passengers who face cancellation or long delays at airports following the terror threat.

Eurostar said all of today's cross-channel services to Paris were full as airline passengers scrambled to reach the continent.

A Eurostar spokeswoman said: "All our London to Paris services today are now full.

"Already they're now getting booked up until lunchtime tomorrow.

"The availability coming in and out of the country is disappearing rapidly as people are trying to get home, or go on holiday."

Eurostar runs 10 trains to Brussels and up to 16 trains a day to Paris, in each direction. Each train accommodates 750 people.

The spokeswoman said: "We're already in high summer season. We were on a busy day anyway and we're rapidly filling up.

"We've been trying to do our best to accommodate large numbers of airline passengers."

Eurostar said it has received 5,000 bookings as a result of "displaced airline passengers". The London to Paris route has sold out today, and there is limited availability tomorrow, Saturday and Sunday, a spokeswoman said.

Travellers are being advised to avoid the long queues building up at railway ticket offices and call Eurostar's contact centres on 08705 186 186 or book online at eurostar.com.

Lines are open from 8am to 9pm Monday to Friday, from 8am to 8pm Saturday, and from 9am to 5pm Sunday.