British Airways is hoping to operate a fuller flight service on Saturday, after three days of freezing fog caused chaos at Heathrow and other airports.
Thousands of passengers have been affected by the fog
Some 46 morning flights are cancelled, but BA plans to operate all afternoon domestic flights to and from Heathrow.
The airline said it hoped to operate 95% of its Heathrow services, including 87% of short-haul flights, on Saturday, with a full service on Sunday.
More than 1,000 flights were cancelled in recent days because of the fog.
Forecasters at the BBC's Weather Centre said they were "reasonably confident" visibility would improve around Heathrow on Saturday, as the fog moved north.
Although Heathrow was the worst affected, other airports including Norwich, Bristol, Cardiff and Southampton have also been disrupted by fog in the past few days, with yet others suffering knock-on effects from Heathrow.
Heathrow managing director Mark Bullock said he was hopeful the situation at the airport would return to "some semblance of normality" on Saturday.
"The picture is a lot better than it has been. On Thursday we had 370 cancelled flights, yesterday that improved to 284, and so far today we have confirmation of 74 cancelled flights, so that's significantly better than it's been," he said.
"We're very hopeful that we can clear the backlog in time for Christmas. British Airways, for example, have been putting on larger aircraft to some of their short-haul destinations, and as of yesterday they've taken over 4,000 people by coach to their destinations and that coaching operation continues today.
"Also the railways are laying on additional train services."
BBC News correspondent Ben Ando, at Heathrow, said people arriving at the airport on Saturday were confident they would be able to catch their flights, particularly if they were booked on medium or long-haul trips.
He said visibility at Heathrow was far better on Saturday morning than it was at the same time the previous day - up to 4,000 metres when it had been down to 600 metres.
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Bmi has made no cancellations at Heathrow and is looking to operate as full a service as possible.
BA flights from Heathrow to Paris and Brussels resume on Sunday.
In all, 411 flights were cancelled on Friday, including more than 300 flights at Heathrow, with all British Airways domestic services scrapped and about 40,000 people affected.
The flight cancellations came about after air traffic control placed restrictions on flights landing and taking off at Heathrow, because of the low visibility.
BA says passengers whose flights have been cancelled are entitled to a full refund.
Mr Bullock defended the handling of the situation at Heathrow where temporary waiting areas in marquees were set up for passengers.
He said: "Nobody wants to see passengers delayed on their journey, especially at this time of year, and our hearts can only go out to those people who have been affected.
"But what we did do on Wednesday when the weather closed in on us was put into place our contingency plans.
"We have heated marquees, we've been providing passengers with catering facilities, we've had video games, televisions and even children's entertainers."
At Gatwick Airport, where many tourist and ski holiday travellers are expected, there are no reported cancellations and most flights are leaving on time, although there may be some delays.
Ken Gibbs from Virgin Trains said there were no problems with its services, although journeys may take longer than normal.
"We're not running any extra services. We have some engineering works - Network Rail are doing some works - so we have some diversions in place, so passengers should expect some extended journey time, I'm afraid," he said.
Brian Bannister from coach operator National Express said the weather had actually helped its services to run on time.
"It's probably been a help to us, strangely. I think it's created nice slow and steady traffic streams across the motorways," he said.
The Highways Agency has suspended more than half of its 83 roadworks, and many rail engineering works are also being delayed until Christmas.