The force has confirmed that "investigations are ongoing" and that it is currently "sifting through CCTV" in response to a local outcry against the damage.
The bench in honour of Wally – who rose to fame in 2016 as Britain's oldest poppy seller - was targeted last month, and despite the writing being cleaned off by three kind schoolboys, it was desecrated again soon after.
Leighton Buzzard Community Policing Team, said on its Facebook page: "Thank you to the residents of Leighton Buzzard. We have now identified the suspects involved in the graffiti/criminal damage.
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"We are currently sifting through CCTV, and are keeping in contact with the organisations which have been affected. If you have any further information please call us on 101 and quote investigation 40/35282/22."
Providing an update, Bedfordshire Police told the LBO: "The location in this post relates to Pulford Road. There have been no arrests but investigations are ongoing, and the community team is working closely with members of the public."
There has been a spate of vandalism in the town recently, with other areas targeted including Oakley Green, and Waterborne Walk.
Damage was also caused to Leighton-Linslade Community Garden.
Leighton-Linslade Town Councillor, Tony Morris, told the LBO: “What is it about this sort of crime that I find so abhorrent? It’s pointless, it’s pathetic, and in the case of Wally’s bench it is totally disrespectful, not just to Wally but to the many people, often volunteers, who strive to keep our town as lovely as it is.”