The Piper PA-28 was in a group of aircraft which was heading to the northern France resort of Le Touquet.
“It crashed into British waters for an unknown reason,” said a spokesman for the French emergency services.
“British Coastguard launched an operation supported by French aircraft and boats including the Abeille-Languedoc (Languedoc Bee) tug, which has been chartered by the French Navy,” he added.
A spokesman for the Maritime Prefecture in France said the wide-ranging search was suspended overnight Saturday, as rescuers said it would resume at first light on Sunday.
“The plane was travelling from Wellesbourne to Le Touquet, with two people on board, before it disappeared off radars,” said the Prefecture spokesman.
Flight records show that that the Piper PA-28R-200 Cherokee Arrow II, registration number G-EGVA left Wellesbourne at 7.56am on Saturday and appeared to go off radar over the Channel at 09.02am.
It has been due to land at Le Touquet, France, but failed to arrive. The plane was built in 1976 and has four seats.
As well as the Abeille Languedoc, the major search involved a French Navy Falcon 50 jet and a Dauphin helicopter.
Ships in the Channel were also alerted to the disappearance, but by nightfall there was no sign of the plane, or any debris.
“The search continued all afternoon, without being able to locate any debris or aircraft wreckage,” said the Prefecture spokesman.
He added: “At the beginning of Saturday evening, without additional elements and the probable sector of disappearance having been fully investigated, the searches were suspended.
“They will resume on Sunday morning morning with a flight by the Dauphin helicopter”.
Those travelling in small planes such as the Piper PA-28 are usually equipped with lifejackets and a life raft.
While the plane may have sunk in the Channel, rescuers are accordingly hoping to find the pilot and passenger on the surface.
The PA-28 is a two or four-seat aircraft built by the U.S. firm, Piper, as a trainer, air taxi, or for personal transport.
It has been in production since 1960 and various models have been involved in a number of high-profile accidents in that time.
In August 1972, Prince William of Gloucester, the Queen's cousin, was killed along with his co-pilot in a Piper Cherokee Arrow after crashing on take-off from Halfpenny Green, near Wolverhampton, during an air race.
