Kent Police believe the man, named as Edvard Stockings or Smith, fell from the Queen Elizabeth II Bridge that crosses the Thames at Dartford, and is searching the water to try to recover him.
The BBC reported that the suspect phoned Leslie Thompson after Lisa Smith, 43, was killed outside The Three Horseshoes in Knockholt, Kent on Friday.
A man accused of shooting his wife outside a pub on Valentine’s Day phoned his friend to tell him: “She’s dead, I love you.
He believed his friend had suffered a breakdown, and had been greatly affected by the death of his father two years ago.
Mr Thompson told the broadcaster he could not understand what had happened.
