“Work will be taking place to replace a banner which was recently vandalised on Farndon Road in Newark,” the authority said.
“We are extremely disappointed that someone would desecrate a banner depicting our national flag.
“Where we can identify those responsible, we will report these sorts of incidents to the police as acts of criminal damage.”
The authority said it did not report the damage in Newark to police.
The cost of the project came under scrutiny when it was announced in October.
Each flag, which have been described by the authority as banners, costs about £457, including brackets, traffic management and cherry pickers.
Barton said they would be reused throughout the year for events such as Armistice Day, Christmas and Easter.