Mr Medina, a professional carer from Chelsea, was the victim of an assault, but a post-mortem examination did not ascertain a cause of death.
Officers were called to the park at around 5.50am on August 12 after a member of the public discovered a man with injuries close to Speakers’ Corner.
He was dead when officers arrived.
Khalaf was unshaven and wore a grey prison-issue tracksuit when he appeared at Wimbledon Magistrates’ Court on Saturday, and spoke through an interpreter to confirm his name and date of birth. He was remanded in custody to appear at the Old Bailey on Tuesday.