Victims of vandalism in Didcot are being urged to report the crimes.
In one incident, a 6ft concrete wall on the corner of Haydon Road and Edinburgh Drive was demolished.
Thames Valley Police claim they are frustrated by of the reluctance of victims to report criminal damage.
In the latest incident, in Edinburgh Drive and adjoining King Alfred Drive, plants and shrubs were also ripped up, but police spokesman Vicky Evans said only one attack had been reported.
Pensioner Granvil Thomas, whose wall in Edinburgh Drive was damaged, said: "Vandals are always kicking odd bits off my front wall. As a pensioner I can't afford to keep repairing the damage.
"It cost me £1,600 on the previous occasion the wall was damaged."
Another pensioner, who asked not to be named, said: "A lot of council tenants don't bother to report walls being kicked over because it happens so often and they know the damage will be repaired by a housing association."
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