By Pascal Rossignol

CALAIS, France (Reuters) -Six people died after a migrant boat trying to cross the Channel from France to Britain capsized early on Saturday, and another two people were possibly missing, French authorities said.

French and UK rescue boats saved nearly 60 migrants and brought them to French or British shores, and search and rescue operations were ongoing, the maritime prefecture said.

Local mayor Franck Dhersin said a large rescue operation was launched at around 6 a.m. (0400 GMT) as dozens of migrant boats tried to make the crossing at the same time.

"Several of the boats were facing serious difficulties," he told Reuters. "Near (the coastal town of) Sangatte they unfortunately found dead bodies."

The Channel between France and Britain is one of the world's busiest shipping lanes and currents are strong, making the crossing on small boats dangerous.

People smugglers typically overload rickety dinghies, leaving them barely afloat and at risk of being lashed by the waves as they try to reach British shores.

Anne Thorel, a volunteer who was on one of the rescue boats, described the migrants' frantic efforts to bail water out of their sinking vessel using their shoes.

"There were too many of them on the (migrant) boat," she told Reuters by phone as she returned to the shore.

Britain's coastguard said it sent a lifeboat from Dover to assist with the Channel rescue, along with a coastguard rescue team and ambulance staff.

A UK Border Force vessel and two lifeboats helped rescue all those on board another small boat in the Channel in a separate incident on Saturday, the British coastguard added.

Prime Minister Rishi Sunak's government has spent the week making announcements about its efforts to reduce the number of asylum seekers arriving in small boats, hoping to win support from voters as the ruling Conservative Party trails in opinion polls.

UK government figures show that the number of migrant Channel crossings so far this year stands at more than 16,000, with over 1,100 people arriving in the past week alone.

In the first three months of this year, most of those on small boats were from Afghanistan, India, Iran or Iraq.

In November 2021, 27 migrants died when their dinghy deflated as they tried to cross the Channel. The accident was the worst accident on record involving migrants in the narrow seaway separating the two countries.

There are more frequent, more deadly disasters in the Mediterranean, where a charity rescue ship rescued 76 migrants on an overloaded wooden boat on Saturday. More than 22,000 people have died or gone missing in its waters since 2014, according to the International Organization for Migration.

(Reporting by Pascal Rossignol in Calais and Ingrid Melander, Tangi Salaun, Christian Hartmann in Paris, David Miliken in LondonWriting by Ingrid MelanderEditing by Helen Popper, Ros Russell and Frances Kerry)