A number of colourful murals on the same street have had red crosses painted over them.
North Somerset Council said the damage to street art on Old Post Office Lane in Weston-super-Mare had been raised with police so “appropriate action” could be taken.
Liberal Democrat council leader, Mike Bell, said he was “fed up” with “mindless” vandalism “masquerading as patriotism” in some cases.
“These vandals are damaging property, making the town centre look worse and adding to the costs on hard-pressed businesses and councils who must clean it up,” he said.