At least three people died after a migrant boat ran into difficulties crossing the English Channel in the early hours, the government has said.

The BBC's Nick Eardley said a person close to the situation said 43 people had been saved, with more than 30 of them rescued from the water.

A major search and rescue operation was launched in waters between Kent and France in freezing conditions.

The home secretary said her "heartfelt thoughts" were with those involved.

The BBC's political correspondent Nick Eardley said the number of deaths could rise further.

It is understood the small boat got into trouble at about 03:00 GMT off the coast of Dungeness, 30 miles west of Dover.

The UK coastguard, the French Navy and an air ambulance were all sent to help with the rescue operation.

A fishing boat in the area and coastguard helicopters from Lydd and Lee on Solent were also involved.

South East Coast Ambulance Service said it was called following reports of the incident, and sent crews to Dover, in Kent, to help with the follow-up operation.

Overnight on Tuesday, temperatures dropped to 1C, with it likely to have been colder out at sea. A yellow weather warning for ice was in place across Kent at the time.