The message “Israel is a terrorist state” was painted on the stone monument just hours after poppy wreaths were left there during a Remembrance Sunday service.
Vandals are believed to have attacked the memorial on Lewisham High Street in South London between midday Sunday and 9am Monday.
The scrawl has since been removed by the local authority.
Calling for witnesses, PC Andrew Dobson of the Met Police said: “Criminal damage and offensive comments of this nature are completely unacceptable and our team are doing all we can to identify those responsible.”
Two teenagers were charged after the Cenotaph in Rochdale, Greater Manchester had the words “Free Palestine” painted on it earlier this month.
One 17-year-old was charged with racially aggravated criminal damage and the other was charged with racially aggravated criminal damage plus an offence of theft.
