Last night the men were described as "very experienced offshore yachtsmen" and friends and family were understood to be "devastated" the search for them had been called off so soon.
The yacht ran into difficulties some 620 miles east of Cape Cod in Massachusetts last Thursday. Contact was lost in the early hours of Friday morning after the crew radioed they they were taking on water and were diverting to the Azores.
US and Canadian aircraft and merchant vessels searched throughout Friday and Saturday but the operation was called off yesterday.
On Saturday a container ship discovered an overturned hull that matched the description of the Cheeki Rafiki but there was no sign of the crew, so the vessel was not inspected.
The four men were sailing the _Cheeki Rafik_i back to the UK for Southampton-based yacht training and charter company Stormforce Coaching.
The US Coastguard were contacted by the yacht’s managers in Falmouth, Cornwall, on Friday. Two personal locator beacons registered to the yacht had been activated, but they have since stopped transmitting signals.
A coastguard spokesman said: "We searched with multiple assets over 4,000 square miles for pings from the vessel’s personal locator beacons. After receiving no more transmissions we believe that we would have found them by now if we were going to find them. These beacons are small devices and the ones being used have a very short battery life."
Weather conditions in the area were described as treacherous, with winds in excess of 50 knots, waves of 15 to 20ft and visibility reduced to under a mile.