London (CNN) -- The chief executive of British airport operator BAA, which is responsible for London's Heathrow, says he will not be taking his bonus for 2010 following the travel chaos caused by heavy snow.

Colin Matthews told CNN: "I am focusing 100% on passengers, we haven't got everyone home yet, there is still a backlog." He refused to comment on the size of the bonus he has declined.

"I do not want to talk about my remuneration. I will be foregoing my bonus for the calendar year 2010," he said. When questioned about a rumored "secret bonus" based on profits, Matthews said: "There is no secret bonus."

BAA would not discuss its bonus schemes but last year Matthews' salary and bonuses totalled £944,000 ($1.45 million), according to the British Press Association.

Asked how Heathrow will respond to the crisis, he said: "It is clear that we will need to buy new equipment... and purchase that as quickly as possible. What has caught us out is the intensity of the snow."

His comments came as tens of thousands of stranded passengers across Europe were finally starting their Christmas holidays Wednesday after airport and rail operators made the most of a clear weather spell and began addressing a huge backlog.

Heathrow, the busiest airport in Europe and one of the hubs most affected by winter weather, opened its second runway Tuesday evening and said it was operating at between 70% and 80% of capacity Wednesday.

However, around 400 flights have been canceled. Travelers were advised to check with their airlines before traveling to the airport.

Malcolm Robertson, head of communications at BAA, told CNN: "We're making progress... 100% of our infrastructure is clear and we're in a good position to increase the number of people we move."

Robertson said that he expected Heathrow to be fully open on Thursday and that the airport was "as prepared as we can be" for further predicted snow later this week.

On Wednesday British Airways said that it would operate a "full longhaul departure schedule" on Thursday and Friday from Heathrow.

Charles de Gaulle Airport in Paris, the second busiest airport in Europe, was also slowly returning to normal. However, forecasted snow on Wednesday forced an expected 15% reduction in flight schedules between 18:00 GMT and 23:00 GMT.

Airlines were expected to cancel one-quarter of scheduled flights on Thursday at Charles de Gaulle, said the Directorate General of Civil Aviation.

At Frankfurt, another major European hub, 1,400 flights were expected to operate Wednesday, according to Juergen Harrer, an airport spokesman. All three runways were open, although there were 70 flight cancellations due to other airports not being operational, he said.

Harrer told CNN, "There are still many passengers in the terminals but we are doing our best to get them to their destinations."

An official at Gatwick Airport, London, also warned of "some knock-on delays and cancellations Wednesday," due to the ongoing impact of snow.

Meanwhile, the long queues that had been winding down the street outside Eurostar's London rail terminal, St. Pancras International, had largely cleared on Wednesday.

A Eurostar spokesman estimated around 500 people were queuing for check-in early Wednesday, far fewer than the thousands seen Tuesday.

"People seem to be respecting our advice not to come to the terminal unless they have a valid ticket for today, and not to arrive more than one hour before their train's departure. This is helping the terminal to get back to normal," Eurostar spokesman Leigh Calder said.

Eurostar has stopped selling new tickets for travel before December 26 in an effort to get pre-booked passengers on trains in time for Christmas.

"We are confident we will get everyone with a valid ticket to their destination before Christmas Eve," Calder said.

Eurostar was running at 80% of normal capacity, taking passengers across the Channel Tunnel to Paris and Brussels, Belgium. Nine trains have been canceled out of 52 scheduled services on Wednesday.

Speed restrictions have been applied, so each journey is taking longer than usual and creating knock-on delays for other services.

The UK's Met Office has issued weather warnings for parts of central England Wednesday but said it was not expecting further snow in London Wednesday and that Heathrow and Gatwick airports "should remain dry."

CNN's Laura Perez-Maestro and Atika Shubert contributed to this report.