Transport Secretary Andrew Adonis said all British airports would reopen at 2100GMT (1700EST), allowing passenger services into the U.K. to resume. Britain's Civil Aviation Authority said all U.K. airspace would reopen at the same time.
British Airways said it hoped to land as many as 25 flights Tuesday evening - from the United States, Africa and Asia into London.
But forecasters said more delays to flights bound for Europe were possible. Airspace in Germany remained largely closed until 0000GMT (8 p.m. EDT) but about 800 flights were allowed to fly at low altitude.
It was the first day since Iceland's Eyjafjallajokull volcano erupted Wednesday that travelers were given a glimmer of hope.
"Everyone was screaming in the airplane from happiness," said Savvas Toumarides of Cyprus, who arrived in New York after getting stuck in Amsterdam for five days and missing his sister's wedding. He said the worst part was "waiting and waiting and not knowing."
"We were in the hotel having breakfast, and we heard an aircraft take off. Everybody got up and applauded," said Bob Basso of San Diego, who has been stranded near Charles de Gaulle since Friday.
The Eurocontrol air traffic agency in Brussels said it expected just under half of Europe's 27,500 flights to go ahead Tuesday, a marked improvement over the last few days. The agency predicted close to normal takeoffs by Friday.
"The situation today is much improved," said Brian Flynn, deputy head of operations at the Brussels-based agency.
But with more than 95,000 flights canceled in the last week alone, airlines faced the enormous task of working through the backlog to get passengers where they want to go - a challenge that could take days or even weeks.
Passengers with current tickets were being given priority - stranded passengers were being told to either pay for a new ticket, take the first available flight or to use their old ticket and wait for days, or weeks, for the first available seat.
"I'm supposed to be home, my children are supposed to be in school," said Belgian Marie-Laurence Gregoire, 41, who was traveling in Japan with her husband and three children, ages 6, 8, 10. They said the best that British Airways could do was put them on a flight to Rome.
"I'm tired. I just want to go home," she said.
Although seismic activity at the volcano has increased, the ash plume appeared to be shrinking Tuesday. Still, scientists were worried that the activity could trigger an even larger eruption at the nearby Katla volcano, which sits on the massive Myrdalsjokull icecap and has erupted every 80 years or so - the last time in 1918.
