Details of which flights will be cancelled will be announced by airlines when they have finalised schedules.
It says parts of Scotland, north-east England and Yorkshire and Humber will be affected by ice and snow, and gave ice warnings in Northern Ireland.
More than 400 flights were cancelled on Friday, with 100 cancelled so far on Saturday.
Heavier snowfalls are predicted for south-east England.
As a result of the disruption, hundreds of people slept on the airport's floor on Friday night.
The flight schedule at Heathrow Airport for Sunday will be reduced by 20%, after 2-6cm of snow was forecast.
More snow has fallen overnight in parts of north-east England, eastern Scotland and Northern Ireland, and drivers are being warned of icy roads across the UK.
Heathrow's chief operating officer, Normand Boivin, apologised to passengers for the Sunday cancellations.
Heathrow's chief operating officer, Normand Boivin, apologised to passengers for the Sunday cancellations.
"Cancelling flights in advance of disruptive weather is a procedure used increasingly around the world, as it means the greatest number of passengers can fly with the minimum amount of disruption," he said.
"Cancelling flights in advance of disruptive weather is a procedure used increasingly around the world, as it means the greatest number of passengers can fly with the minimum amount of disruption," he said.
South West Trains has published a revised timetable and is not running a service on certain routes
A woman was killed following a crash involving a number of vehicles in bad weather on the A1 at Little Ponton, near Grantham on Friday
Drifting snow
Some are angry, some are laughing it off, but most look tired and frustrated.
Each passenger has their own story, a birthday trip to Paris cut short, a skiing holiday hanging in the balance, a long flight home delayed indefinitely.
"You get two inches of snow? We get two feet" says a man from up state New York, adding that the disruption it causes here makes him "giggle".
For some it is a second frustrating day in the terminal. Sleep is not easy under fluorescent lights on a hard concrete floor. Airport staff seem to be eager to help, but they cannot bring much good news to those who just want to know when they can fly.
Although the congestion has eased, there is a warning more snow will cause more delays.
Jamie Methuen was supposed to fly to Geneva on Friday and then travel to France for a skiing weekend.
He told the BBC his flight was cancelled after a four-hour wait at Heathrow, and that he would have "appreciated a far more honest and pragmatic approach" from the airlines, "four hours earlier".
"They really should have given more thought to the relative likelihood of the flight operating. If I were a betting man, I wouldn't have bet that flight was [going to be] operating at 10 o'clock at night."
A spokeswoman for Heathrow's operators BAA said on Saturday that "the airport is operating as usual".
Drifting snow
The Met Office has issued a yellow warning, which means "Be aware", for ice across much of the UK. In particular, Northern Ireland, parts of Scotland, north-east England and Yorkshire and Humber are due to be affected.
Friday's snowfall reached 26cm (10in) in Sennybridge, in Powys, while elsewhere there was 16cm in Filton, near Bristol, 12cm in Brize Norton, Oxfordshire, and 10cm in Nottingham, according to the BBC Weather Centre.
Forecaster Mike Silverstone said the snow was easing in most places, although Saturday would see light flurries.
Forecaster Mike Silverstone said the snow was easing in most places, although Saturday would see light flurries.
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The heavy snow forecast across parts of north-east England, eastern Scotland and Northern Ireland could bring 5-10cm, he said, but was due to ease during Saturday.
"Most places will be around or below freezing, so there will be no or little thaw," he added. "There will be quite a breeze, which means there could be snow drifts."
"Most places will be around or below freezing, so there will be no or little thaw," he added. "There will be quite a breeze, which means there could be snow drifts."
He said Sunday would see mostly light snow confined to the southern half of the UK, adding: "But we could see something a bit heavier in the south-eastern corner."
Friday's snowfall reached 26cm (10in) in Sennybridge, in Powys, while elsewhere there was 16cm in Filton, near Bristol, 12cm in Brize Norton, Oxfordshire, and 10cm in Nottingham, according to the BBC Weather Centre.
The AA warned drivers to take extra care on the roads.
The AA warned drivers to take extra care on the roads.
For more information on the weather and transport situation in your area, visit the BBC Weather website and BBC Travel News.
For more information on the weather and transport situation in your area, visit the BBC Weather website and BBC Travel News.
Have you been affected by the snow? Are you making preparations for the coming days? Please send us your comments using the form below.
Have you been affected by the snow? Are you making preparations for the coming days? Please send us your comments using the form below.
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