Europe's airspace reopened for business as Iceland's volcano lost its fury yesterday, leaving passengers scrambling to get home and recriminations flying over the $1.7 billion cost of the crisis.

Three-quarters of flights scheduled in Europe were on track to fly, said the body coordinating air traffic across the continent, a week after a volcanic eruption in Iceland caused the worst disruption to aviation since World War II.

While experts in Iceland said the Eyjafjjoell volcano had lost most of its intensity, airline bosses were frantically adding up the cost of the crisis which their umbrella body said had cost $400 million a day at its peak.

All of Europe's main air hubs were up and running yesterday and the Europe-wide coordinating body Eurocontrol said it expected some 21,000 flights to take place in European airspace, against a typical 28,000.

In Europe's far north, Helsinki in Finland and airspace over the remote Scottish isles of Orkney and Shetland were temporarily reclosed due to still unsafe ash levels. But Iceland's other Nordic neighbours Norway, Denmark and Sweden lifted the last of their flight restrictions in a sign the worst of the threat had faded.

Millions had their travel plans affected since governments closed their airspace last Thursday and IATA, the body representing the global airline industry, put the overall cost at 1.7 billion dollars (€1.3 billion).

European governments "must take their responsibility" and help the carriers, said IATA chief Giovanni Bisignani.

British Airways chief executive Willie Walsh had branded the ban unnecessary, with the disruption heaping more misery on an airline reeling from a recent strike.

Flights were finally cleared for landing at London's Heathrow airport on Tuesday night, but BA flew around two dozen long-haul planes back to Britain even before the no-fly zone was lifted.

Some were initially turned away and forced to land at other airports but there were scenes of jubilation on other planes when pilots announced they had been cleared to land at Heathrow, Europe's busiest airport.

British opposition leader David Cameron - who is challenging Labour leader Gordon Brown for the premiership next month - called for a public inquiry into the "muddle and confusion" in the government's handling of the crisis.

British Airways said they were hoping to operate all longhaul flights from Heathrow and Gatwick as normal yesterday.

Wolfgang Mayrhuber, the head of Lufthansa, said his firm expected to operate around 500 flights, a third of its normal service.

Dutch airline KLM expected to resume all intercontinental flights to and from Amsterdam Airport Schiphol, and about 70 per cent of flights in Europe.

All long-haul passenger services from Paris' main international hub Charles de Gaulle were operating as scheduled, airport officials said, while Air France said it had flown 40,000 stranded people back home since Tuesday.