Planes took to Europe's skies in greater numbers Wednesday after the chaos caused by the Iceland volcano cloud, but travellers still faced disruption as airlines fought to shift a huge backlog.

Britain finally lifted a flight ban on its airspace late Tuesday, following Belgium, France and Germany and others in easing restrictions introduced after the Eyjafjoell volcano spewed a huge dust cloud across the continent.

Shortly before 10:00 pm (2100 GMT), a British Airways flight from Vancouver flew into Heathrow airport, Europe's busiest air hub.

It was the first to land there since officials closed down the country's airspace last week.

Stranded travellers across Europe were delighted as the curbs on flying were eased.

"I've never been so happy in my life going back home," said Shahriar Ravari from San Diego, waiting at a Paris airport for a flight to Los Angeles, the end of his travel nightmare in sight.

"I love France but to be going home is something else."

But the airlines now face a huge challenge to shift the backlog of passengers that has built up.

Millions of people have been stranded across the globe since Europe began shutting down airspace on April 14, and airline schedules are in disarray after so many of their planes were grounded.

"As we have many aircraft and crew out of position, it will still take some considerable time before we can restore our full flying programme," British Airways warned.

Budget carrier easyJet added: "Due to the extent of the disruption, it will take several days to resume normal operations and delays are likely."

IATA, the International Air Transport Association, says the crisis cost the industry 200 million dollars a day.

And IATA chief Giovanni Bisignani told Italian television that more than five medium- and small-sized European airlines risked bankruptcy in the fall-out from the ash cloud shutdowns and called for EU compensation.

In a sign of mounting tensions between airlines and the authorities, BA Tuesday sent a fleet of long-haul flights to land at Heathrow before restrictions had been lifted, attacking the continued ban.

One of the planes had to divert to Brussels, but shortly afterwards the airspace was opened and aircraft began to land.

Eurocontrol, the body coordinating air traffic control across the region, said almost three-quarters of European airspace was open late Tuesday, although less than half of scheduled flights were set to take off.

It expected 13,000 flights of the normal 28,000 in European airspace to take off Tuesday.

German authorities extended the no-fly period to 0000 GMT Wednesday but pilots are allowed to fly in the interim at certain altitudes during daytime when they are not reliant on instruments and can use their own eyesight to avoid other planes.

Lufthansa said it planned to carry more than 15,000 passengers on some 200 flights: around 11 percent of its normal daily schedule.

Airspace over northern Italy slowly reopened with the flights leaving Rome and Milan. Flights also began landing at Belgian airports. Norway reopened all of its airspace while keeping a weather eye on the ash cloud.

In France, Transport Minister Dominique Bussereau said 30 percent of scheduled national and international flights would fly from Paris airports.

Sweden kept its airspace closed, while Denmark said it would temporarily reopen most of its airspace and airports, including Scandinavia's largest airport in Copenhagen, from 0000 GMT to 0900 GMT Wednesday.

Finland's airports will remain closed until 9:00 am (0600 GMT) Wednesday, airport operator Finavia said, extending a previous forecast.

Finnish officials however said late Tuesday they would open airspace at altitudes above 9,500 metres (31,000 feet) for international traffic overflights until 9:00 am (0600 GMT) Thursday.

Airlines outside Europe reacted differently.

While Australia's Qantas Airways extended its ban on flights to and from Europe for another 24 hours, Air China said it had resumed routes between Beijing and destinations including Moscow, Stockholm and Rome.

In Iceland itself, police said the plume of ash from the Eyjafjoell volcano -- which began erupting last Wednesday -- was diminishing but warned that there was "still considerable volcanic activity at the site."

The World Meteorological Organisation said the ash was expected to head towards the Arctic when the weather changed later in the week.