I think the ship was sunk in the early evening of 28 January. These two links tell the story.
https://www.warsailors.com/singleships/bjornvik.html
https://www.warsailors.com/singleships/bjornvik2.html
The second link has details coming from a February inquiry into the loss and includes testimony from two of the three survivors (who were rescued the next day).
The ship was part of convoy WP.103. The Bjornvik had problems keeping up and had dropped well behind the convoy (which was out of sight). At 18:30 on the 28th the ship was attacked, and it sank in 30 – 40 seconds. There was no time to even fire off any rescue rockets. The three survivors managed to get into a rescue raft but were taken further out to sea and were rescued after some 17 hours adrift by a passing ship.
I think the Admiralty was not aware that the ship had been sunk until the 29th