Airlines including Air France, Lufthansa, British Airways, Ryanair and Qantas announced restrictions to their schedules in Europe because of the ash, which experts have said can stall engines and cause electrical failures on board aircraft.

Forecasts suggest the cloud of ash will persist and that the impact will continue for at least the next 24 hours, Eurocontrol said Saturday morning.

The measures were choking international travel and stranding thousands of passengers across the globe.

Restrictions on United Kingdom-controlled airspace will remain in place until at least 7 a.m. Sunday with restrictions in spome parts of the country forecast to remaining in place for another 12 hours.

It was a chaotic scene Saturday morning at London's Heathrow airport. At Terminal 3, which serves long-distance destinations like New York, South Africa and Washington, passengers complained they were getting no proper communication from their airlines.

Flight staff were handing out leaflets, and some of the airlines were rebooking passengers on later flights.

It was busy, too, at the ferry port in Calais, France, where passengers were hoping to catch a ride across the English Channel.

"The walk-in terminal in Calais is manic," said Alasdair Russell, who went to Calais from central England to pick up a friend's father. "The car park outside is full of people trying to hitch lifts. It's fairly mental."

The line for tickets didn't appear to be moving, Russell told CNN.

P&O Ferries, one of the largest cross-channel ferry operators, said it was receiving record calls and bookings and could not accept any more reservations on the Dover-Calais route until Wednesday.

The company normally gets a few thousand calls a day, but by lunchtime Friday it had logged more than 30,000, P&O said on its Twitter feed.

SeaFrance Ferries, another major operator, said it had "overwhelming demand" for reservations and was limiting the number of foot passengers it could take on board.

Russell, who is traveling by car, said his friend's father arrived in Calais from Portugal, having paid 2,000 euros ($2,700) to a private chauffeur to get there. The ride took 20 hours, Russell said.

Peter Brown, the founder of Brown's Chauffeur Hire in London, said he is seeing similar fares as passengers who can't fly try other means to get to their destinations.

He told CNN passengers have booked trips to Lisbon, Portugal; Cannes, France; Duesseldorf, Germany; Zurich, Switzerland; Brussels, Belgium; and Paris and Lyon in France.

"The longest journey was two and a half days to Lisbon," he said. "It required an overnight stay and the whole journey totaled 4,000 pounds ($6,150)."

Businessman J.P. Brommel was attending a TV conference in Cannes, France, when the problems began and said he has been unable to return home to New York.

Many of the 11,500 attendees at the conference who found themselves stranded have resorted to driving rental cars long-distance to get home, but one problem is that it's spring break for many countries in Europe.

"Even if you can rent a car, if you can find one, you're going to be dealing with a tremendous amount of traffic on the highways here, so it's just a touch and go situation," Brommel told CNN.

Others are trying to drive to nearby Toulon to catch the high-speed TGV to Paris, or driving to Madrid, Spain, where they hope to catch flights home, Brommel said.

The ash cloud is drifting south and eastward over Europe. Although barely visible in the air, the ash -- made up of tiny particles of rock, glass and sand -- poses a serious threat to aircraft.

Past incidents of aircraft trying to fly through volcanic ash clouds and suffering damage and engine failure led European officials to shut their airspaces rather than risk a catastrophe, said Joe Sultana, an official at Eurocontrol, the intergovernmental body that manages European air travel.

"I cannot say whether it's an overreaction or underreaction," Sultana said Friday. "I think everybody is working in the interest of safety. We understand the impact to the airlines ... but safety comes first."

Travelers rush to trains and ferries

Airline analyst Jamie Bowden, standing outside Heathrow where planes were parked at the gates, told CNN he had never seen a situation like this.

"I've been in the business for more than 30 years and I've never known Heathrow Airport to be this quiet," Bowden said. "This kind of disruption is unprecedented. I think this will be going on for at least eight to 10 days before it starts settling back to normal."

The volcano was still erupting and spewing ash Saturday, said Agust Gunnar Gylfason, a project manager at Iceland's Department of Civil Protection and Emergency Management.

"We cannot tell how long an eruption like this will go on," Gylfason said.

The eruption began March 20 beneath the Eyjafjallajokull glacier in southern Iceland, blowing a hole in the ice. It worsened this week, forcing local evacuations and eventually affecting European airspace.

When the volcano last erupted in 1821, the eruption lasted on and off for two years, Gylfason said.

Experts: No end to volcano ash in sight

The closures in Europe were having an effect worldwide. There were delays and cancellations Saturday at all 10 of Russia's international airports, including those in Moscow and St. Petersburg, the Russian Transport Ministry said.

The Russian national railway company RZHD added extra cars to trains running between Russia and Europe, the company said.

Spain's national railway RENFE said the few trains that run north to France daily were not full because a strike by French engineers had caused delays.

Spanish airports were operating but experiencing delays in flights to northern Europe, the Spanish air traffic authority AENA said. As of 7:30 a.m. (1:30 a.m. ET) Saturday, AENA said 708 flights had been canceled between Spain and northern Europe out of a total of 2,300 -- a figure representing 30 percent of all scheduled flights.

Airport authorities have increased cleaning and medical services to accommodate stranded passengers, and have asked food vendors to stock up and stay open for longer, AENA said.

CNN's Melissa Gray, Bharati Naik and Cristina Lynch in London, England; Maxim Tkachenko in Moscow, Russia; and Al Goodman in Madrid, Spain, contributed to this report.