Mr Voyce set off during the storm to go home, which was about eight miles (13km) away in Alnwick, the inquest was told.
Det Con Victoria Henderson, from Northumbria Police, said he drove over a ford at speed, breaking his number plate in the process, and became stuck in the high water.
Despite trying to reverse, the vehicle was washed away, the inquest heard. It was found the following day.
The Toyota was found in reverse gear, which led to the belief that Mr Voyce may have tried to go back the way he came when the vehicle stalled.
She said it was unclear if Mr Voyce had tried to get out of the vehicle himself or if he had been swept away by the force of the water.
Det Con Henderson said a ford warning road sign would have been visible but the depth pole showing the height of the flood was submerged on the other side of the crossing.