The annual Christmas test of the country's transport network began yesterday, with millions of people descending on roads, railway stations and airports to stretch the system to its limits.

Roads around London were packed with traffic by mid-afternoon and were expected to remain under heavy pressure until Christmas Eve, while domestic and Eurostar train passengers grappled with strikes and airport departure halls were said to be "heaving".

In what might have been a triumph of hope over experience, motoring organisations advised people to travel on Christmas Day, when they could be sure of an easy journey.

As the build-up began on the M25 and the M5, a spokesman for AA Roadwatch warned drivers to watch out for icy roads. Severe weather was forecast for the weekend.

"We expect a significant number of Britain's 23 million cars to be on the roads between now and Christmas. Saturday and Sunday will be busy, particularly around out-of-town shopping centres, and Christmas Eve will probably be the busiest day, as it is every year.

"The best day to travel is definitely Christmas Day. We would advise that if your relatives live quite close by, you should travel then because you won't find yourself stuck in heavy traffic," the spokesman said.

With Christmas Day falling on a Tuesday, giving people four days to make their journey, there was reason to hope that people might heed the calls to stagger their trips.

Rail operators were expecting two million passengers this weekend and 70,000 people went through Paddington station yesterday.

Two companies began the holiday dealing with industrial actions. Eurostar cancelled 15 of its 55 scheduled services yesterday from Waterloo to Paris and Lille because of stoppages by train drivers in Lille and Aslef staff in London. Passengers who had tickets for cancelled trains were given places on other services but disruption is likely to continue because the French industrial action continues until tomorrow. A Eurostar spokeswoman said: "At the moment everybody who wanted to travel has been able to and given everything else being equal that should continue. We are bullish for the weekend but there may be one or two cancellations."

Virgin Trains was hit by a 24-hour stoppage by station staff in the RMT rail union over changes to pay and shift patterns, but a spokesman said all trains would run as normal. "Extra trained staff have been brought in to cover their duties. We will get by and will run a service as normal, we will not come to a stop," he said.

Airports saw a welcome return of crowds that had stayed away since 11 September, with the concourse at Gatwick's south terminal said to be "absolutely heaving" yesterday. The extra baggage of Christmas travellers added to the difficulties of tightened security. At Stansted airport, where 400,000 people are expected to take flights by 2 January, passengers have been advised to leave Christmas presents unwrapped for security checks, and to ask their airline if Christmas crackers are allowed on the plane.

Weather forecasters predicted snowfall over eastern England and Scotland at the weekend, leading bookmakers to offer the shortest price on a white Christmas for 20 years. A PA WeatherCentre spokesman said: "Scotland remains the most likely place for snow on December 25, while there is also a chance of a white Christmas in the north of England. In the south we expect it to be breezy and cloudy with a bit of rain. Boxing Day has the greatest chance of getting snow over the festive period."

William Hill cut the odds on snowfall in Glasgow from 11/4 to 6/4. London and Manchester were at 11/4 with Cardiff the 7/2 outsider.