German authorities have called off the search for four crew members missing after their British-flagged cargo ship sank following a collision with a larger vessel in the North Sea.

The Verity, which had seven people on board and was en route from Bremen to the port of Immingham on the east coast of England, sank shortly after the crash, which happened about 14 miles (22.5km) south-west of the German island of Heligoland a little before 5am on Tuesday.

Two sailors were rescued and the body of another was recovered.

Rescue ships and aircraft participating in the search were unable to locate the four missing crew members on Tuesday, and divers sent down to the wreck of the Verity to check for any signs of life were unable to find anything.

Officials said the water temperature at the time of the collision was about 12C (54F), which experience has shown people can survive for about 20 hours.

Germany’s Central Command for Maritime Emergencies said the entire sea area where the missing sailors might be was searched again during the night without results, and rescuers then stopped the search.

It said search efforts on the surface will not be resumed on Wednesday but the emergency command will consider “what measures can be taken around the site of the accident in the course of the day”.

The larger cargo ship involved in the collision – the Bahamas-flagged Polesie, which had 22 people on board – was able to reach the German port of Cuxhaven under its own steam.

There has been no word on the cause of the collision.