Cross-Channel rail operator Eurostar is urging people to avoid London St Pancras station unless they have a pre-booked ticket.
Most of the firm’s train services on Friday were sold out as many people brought their Christmas travel plans forward after the new coronavirus restrictions were announced on Thursday.
Ferry operators and airlines have also experienced a surge in demand.
The French prime minister, Jean Castex, said tough restrictions will be enforced from Saturday, including a requirement for “compelling reasons” to travel to or from the UK.
Trips for tourism or business will not be permitted.
Castex’s office said this is “in the face of the extremely rapid spread of the Omicron variant in the United Kingdom”.
All arrivals in France will need to provide evidence of a negative coronavirus test taken less than 24 hours in advance, and must isolate for at least two days.
Hauliers are exempt from the new rules.
Travel firms described the tourism ban as a “hammer blow”.
