Demonstrations following his death saw a statue of royal prince Ras Makonnen Wolde Mikael, the father of Selassie, Ethiopia’s last emperor, torn down in the eastern city of Harar.
Hachalu’s songs focused on the rights of Ethiopia’s Oromo ethnic group and he had been a prominent voice in anti-government protests that led to a change in leadership in 2018.
Wimbledon resident Andrew Morris told the Press Association he had seen a mostly male group in the park, carrying fliers with Oromo slogans, while out walking his dog.
“I heard the statue being smashed up, but didn’t actually see it happen,” he added.
The Metropolitan Police said inquiries were ongoing and no arrests had yet been made after they were called to a report of criminal damage at 17:10 BST on Tuesday.
Selassie lived in Wimbledon in 1936 during his exile following the Italian invasion of his country. The statue was sculpted by Hilda Seligman, while he stayed with her family, and later erected in Cannizaro Park.