Snow and ice caused problems on railways and roads. Forecasters predicted more snow and ice in the next 24 hours.
Cross-Channel Eurostar trains began running between London and continental Europe on Tuesday after four days of cancellations blamed on powdery snow left tens of thousands stranded just before Christmas.
However, severe winter weather caused chaos at airports across Europe with flights delayed or cancelled in Italy and Germany. Snow and ice caused problems on railways and roads. Forecasters predicted more snow and ice in the next 24 hours.
Eurostar trains were cancelled after 2,500 people were trapped for up to 16 hours on Saturday in the undersea Channel Tunnel with no power, air conditioning, food or water — bringing a storm of anger down on the company.
A limited service resumed on Tuesday when a Eurostar train left London's St Pancras International station at 7.41am. (07.41 GMT) heading for Paris. An earlier train had set off in the other direction from Gare du Nord station in Paris with about 1,000 passengers still queuing for later trains.
Some among about 500 people queuing at St Pancras shouted at Eurostar staff, complaining about a lack of information.
Eurostar said that it was clearing the backlog quicker than expected and invited customers with tickets for Tuesday to head to the station in the hope of getting them moving.
Eurostar, owned by the French and Belgian state railway firms and by Britain, has given priority to passengers with tickets from previous days.
The Christmas season is one of the busiest of the year and snow and ice disrupted air, train and road travel.
Britain's airports were recovering from a backlog but travellers were warned there could be delays and cancellations.
Roads were also severely hit with Britain's AA breakdown service reporting a record 16,000 breakdowns on Monday.
Italian national carrier Alitalia restarted flights from Milan's Linate airport, while the bigger Malpensa airport resumed flights in early afternoon after disruptions.
Berlin's Tegel Airport in Germany was closed for an hour, and more than 200 flights were cancelled at Frankfurt.
About 400 stranded passengers spent the night at Amsterdam's Schiphol on improvised beds.
In France, 12 people have died this month in the severe cold, a homeless group said.
A Eurostar spokesman said its backlog was "considerably" less than 40,000 because some had flown home. Others returned by coach or ferry.
He admitted the company had taken some "reputational damage" over the last couple of days, but he blamed "a unique combination of climatic conditions in northern France" and ice.
When the trains entered the warm tunnel, a huge amount of condensation built up, causing a short-circuit, he said.
France's government doubted the cold was the sole reason and has ordered an investigation.
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