The Grade II listed memorial has stood in Lower Green West, Mitcham, since 1920 and has inscribed on it the names of 588 people who died during the First World War.
According to the Local Democracy reporting service, the alleged theft was discovered in mid-June but it is not known when the swords went missing.
On advice from Merton council and Historic England, Tony Burton from the Mitcham Cricket Green Community and Heritage group reported the incident to the police as a heritage crime on Wednesday.
Mr Burton said: “They have been removed in a fairly robust manner, they have been wrenched off so I don’t know if there is any other damage.
“The swords are an integral part of the memorial, there were four of them and three have disappeared.
“For such brutal vandalism to be caused is a shock to the system. It is such an important memorial and part of the area.
“We got it nationally listed very recently, in 2017, that shows it is important and also means any damage it a criminal offence.
“We are going to be in touch with the war memorial trust, we are looking at what options there are to get funding to get a replacement.”
On the advice of @HistoricEngland & @Merton_Council we've reported the loss of three bronze swords from the Grade II listed war memorial as a heritage crime to @metpoliceuk. We are exploring options for their replacement - the memorial was originally funded by public subscription pic.twitter.com/gx4WHoPYVz
— Mitcham Cricket Grn (@MitchamCrktGrn) July 20, 2022
Councillor Eleanor Stringer, Merton council’s cabinet member for civic pride said: “We’re extremely disappointed that the swords have been removed from the war memorial at Lower Green West, and we will work with Mitcham Cricket Green Community and Heritage to help them replace them.”
The memorial was unveiled in November 1920 at a ceremony attended by 5,000 people.
It was restored in 1962, with an additional panel added to pay tribute to those who died during the Second World War.
The sculpted bronze swords are a point of “architectural interest” and were awarded listed status by Historic England in 2017.
The Metropolitan Police confirmed they are investigating a theft in relation to the incident.