(CNN) -- Forecasters say the United Kingdom will remain in the grip of bitter winter weather through at least Monday.
"Heavy snow showers Sunday will affect northeast England and eastern parts of Scotland as a snow system comes in off the North Sea," said Met Office Special Forecaster Tony Burgess. "Southern England should not see much snow Sunday, Heathrow and Gatwick will hopefully improve, and northern Ireland will see a bit of respite," he said.
Burgess added that another series of weather systems will move into the area, warning, "There is another risk of [heavy snow] across England and south Wales on Monday."
A spokesman for Heathrow airport operator BAA told CNN, "We have a team working very hard around the clock to do everything to prepare the airport for operation." BAA is sending similar information out as Twitter messages.
Frigid temperatures and extreme conditions continued to pummel Europe Saturday. Snow, ice and fog have caused travel chaos ahead of a busy holiday travel week.
From Northern Ireland to Bulgaria, blizzard conditions left airports with heavy delays or shut them entirely.
London's Heathrow and Gatwick airports closed all runways Saturday afternoon because of heavy snow and ice, though Gatwick reopened at 3 p.m. after clearing 4 inches of snow from the tarmac. Despite the reopening, the airport warned of "inevitable" delays and cancellations throughout the day.
British Airways canceled all Saturday domestic and European flights at Heathrow. On Saturday night the airport announced it would be closed indefinitely.
All easyJet and British Airways flights -- with the exception of a flight to Egypt -- were canceled out of Gatwick as well.
Police closed several access roads surrounding the airports due to dangerous driving conditions.
The delays and cancellations extended across Europe -- to Amsterdam, the Netherlands; Geneva, Switzerland; Munich, Germany; Paris, France; and Copenhagen, Denmark.
Heavy snowfall also forced the closing of Hungary's Budapest Ferihegy International Airport on Saturday. It had reopened by 4:30 p.m.
The relentless weather caused approximately 250 flights to be cancelled and thousands of passengers stranded at Amsterdam's Schiphol airport on Friday, according to airport spokeswoman Antoinette Spaans.
"We are expecting more delays due to weather conditions," Spaans said Saturday. "The most delays and cancellations are expected to affect air traffic within Europe," she added.
Katherin Kujit and her husband spent four hours at Schiphol and still didn't make their flight.
"Some people seemed very calm, but many were agitated," Kujit said. "You could not sit, suitcases everywhere. People squashed closely together because they don't want to lose 4 inches in line."
They eventually gave up and booked a Monday flight to the United States.
Ireland braced for an icey Saturday as the Irish Meteorological Service, Met Eireann, forecast widespread frost, ice and freezing fog for the morning, and some sleet and snow showers for later in the day. Temperatures were expected to drop down to between 4 and 8 degrees Celsius below zero (between 18 degrees and 25 degrees Fahrenheit) Saturday night.
Northern Ireland was blanketed at the end of this week with its worst snowfall in 25 years, according to CNN affiliate TV3.
The government issued emergency snow warnings Friday night, and more snow was expected Saturday.
The Police Service of Northern Ireland warned motorists to avoid treacherous roads and travel "only if absolutely necessary."
A British Airways flight from Boston and bound for London's Heathrow airport was flying over Ireland when passengers looking at their seat-back video screens noticed the map showed their plane making a U-turn. The aircraft later landed in Reykjavik, Iceland. Passengers alternately groaned and laughed when airline officials told them they had no idea when the flight to the United Kingdom could continue.
At Frankfurt Airport Saturday approximately 240 flights were canceled and delays are expected to continue, according to airport officials.
Airport personnel worked frantically Saturday morning to de-ice airplanes and return the airport to full operations, Ross said. He added that while about 3,000 passengers were stranded Friday, after having passed through passport control, the situation has improved Saturday and that stranded passengers were provided food and water for the wait.
Travelers were experiencing similar delays in Berlin.
"Our holiday plans seem to be on the verge of being frozen for now," said Arundhati Banerjee of the United Kingdom, who was stranded at the airport.
Meanwhile in Bulgaria, the eastern part of the country has been under snow for three days, with accumulation at nearly 1 meter (40 inches) in some areas, according to CNN affiliate bTV.
The main highway, airport and port in Varna, Bulgaria, were closed Friday for several hours. Four regions in Bulgaria -- Silistra, Dorbich, Varna and Burgas -- elevated the weather advisory, and the country was still expecting heavy snowfall and strong winds, bTV's website said. Many roads remain closed, and town and villages were without water or electricity.
In Belgium, the weather forced truck drivers to spend a freezing night in their cabs after authorities banned trucks over seven tons from travelling on icy roads.
Italy's ANSA news agency reported that two people had died because of the bad weather -- a truck driver who was killed in a car accident and a man who died of a heart attack while cleaning up snow outside his house. Hundreds of passengers were stranded in Florence, Italy, after snow and ice stopped high-speed trains from entering the city's train station, the agency said.
In northeastern Greece near Macedonia, heavy snowfall mid-week caused massive problems on several highways, where snowchains were declared mandatory, according to national news Athens News Agency.
Meteorologists say the cold weather is caused by a negative phase of the Arctic Oscillation, which means that cold Arctic air is flowing into southern latitudes that are normally much warmer.
Forecasters don't expect conditions to change anytime soon. The next wave of snowy weather is expected to bring up to 20 centimeters (8 inches) to some parts of the U.K., with London expected to receive 5 to 10 centimeters (2 to 4 inches) of snow.
The weather system will move across France and Germany on Saturday night and Sunday. Below-normal temperatures are expected to continue in northern Europe into the beginning of next week.
CNN's Kathryn Tancos, Mila Sanina, Boriana Milanova, Hada Messia, Per Nyberg, Peter Taggert and Charley Keyes contributed to this report.