The incident happened in the Town Foot area of Rothbury shortly before 11.30pm on Thursday, June 3.
A Northumbria Police spokesperson said: “It was reported that a vehicle had collided with a wall and telegraph pole, causing substantial damage, before the occupants left the scene on foot.
“An investigation has been launched into the incident with enquiries ongoing to locate those involved. Officers would ask those involved to come forward and contact police immediately.
“Anyone with information is asked to contact police via the ‘Tell Us Something’ page of our website or by calling 101 quoting log 1248 030621.”
Rothbury county councillor Steven Bridgett said: “They must have been going at a hell of a speed to do that kind of damage.
“The damage caused will run into thousands of pounds. The Victorian style lighting column alone cost over £4,000 to install.”