The incident happened in Mountsfield Park in Stainton Road at 1.20pm yesterday (November 14).
Officers were dispatched to the scene, where a 43-year-old man was found suffering a facial injury.
The victim reported he had been punched in the face by a man who had since left the scene.
A 30-year-old man has been arrested on suspicion of assault and remains in custody at this time as enquiries continue.
A spokesperson said: “Police were called at 13:20hrs on Friday, 14 November to Mountsfield Park, Catford to reports of a man being assaulted.
“Officers attended and found a 43-year-old man with an injury to his face. The victim reported being punched in the face by a man who then left the scene.
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“The victim did not receive medical treatment at the scene.
“A 30-year-old man has since been arrested on suspicion of assault and remains in custody.”
Anyone with information is asked to contact police on 101 or online quoting CAD 3793/14Nov, or you can contact Crimestoppers anonymously on 0800 555 111.

