Packed Eurostar trains began to haul thousands of angry passengers between Paris, Brussels and London on Tuesday as the firm started to clear a backlog of 75,000 stranded by a winter weather shutdown.

The normally high-speed Channel Tunnel service, once seen as a triumph of European engineering, was brought shuddering to a halt on Friday by what a British spokesman called a fall of "fluffier" than expected snow.

Thousands of passengers watched at London Saint Pancras, Paris Gare du Nord and Brussels Midi stations as the first trains pulled away, each filled to capacity with 750 ticket-holders who had been due to travel at the weekend.

Amid the anger of those forced to wait, there were moments of relief as the first passengers arrived in London from France, three days late. As night fell on Tuesday the crowds had at last begun to thin out.

"We have been pretty successful in clearing the backlog of passengers who have been waiting to travel since both Saturday and Sunday," Eurostar chief executive Richard Brown told a news conference in London.

He said passengers holding tickets from Monday were now being allowed to travel on Tuesday, as the crowds of people waiting to travel had thinned out more quickly than expected.

Two-thirds of trains were running on Tuesday, and Eurostar said it would continue to operate a restricted service on Wednesday and Thursday.

"Customers with tickets for travel between Saturday 19 and Thursday 24 December can come to the terminal on either Wednesday or Thursday and we will do our best to allocate a seat on the next available train," a spokesman said.

At least one traveller managed to get on board in the northern city of Lille with a Tuesday ticket.

"I've been incredibly lucky to get through," admitted school headmaster Gregory Mollet, arriving in London with his 12-year-old son.

"I am going to see Paul McCartney in concert tonight, so it was something I didn't want to miss."

Those still stuck abroad ahead of the Christmas break were less positive.

Annelise Pemers, a 27-year-old Belgian credit controller trying to get to her parents' home in Brussels, said: "We're sitting here because we've been told to come back tomorrow. The situation is totally unacceptable.

"I heard they said it was because of the wrong type of snow but they need to put plans in place to deal with that, and the information from Eurostar has been terrible," she told AFP at Saint Pancras.

Politicians on both sides of the Channel have criticised the train operator -- a consortium of a British firm and the French and Belgian state networks -- for what is seen as its disastrous response to the breakdown.

Some 2,000 passengers were trapped in the tunnel under the English Channel on Friday night, many of them for hours on end, without food, drink, adequate sanitation or news of when or how they would be rescued.

On Tuesday, the French rail firm SNCF took out a full page ad in national papers in an attempt to explain what had happened and to defend its role.

"Tests carried out on Sunday showed that short-circuits were caused by an exceptionally fine and powdery snow. It built up in the motor compartments and brutally condensed on entry to the tunnel," it said.

Temperatures plunged on Friday, as northwestern Europe was gripped by the first cold snap of the season, but in the undersea tunnel between France and Britain it is 25 degrees Celsius (77 degrees Fahrenheit).

"Eurostar's board has decided to order an independent inquiry. It will explain why the operations to get people out of the tunnel and on to London took so long and were accompanied by so little information," it said.

"Corrective actions will be put in place," the statement promised.

With a limited programme of departures -- only two out of three services are operating -- the company hoped to carry 26,000 passengers on Tuesday, whereas at least 75,000 have seen their travel plans disrupted by the breakdowns.

Eurostar said it did not expect services to be back to normal before Christmas Day on Friday.