Roger Sylvester, 30, was held under the Mental Health Act after a disturbance at his home in Tottenham, north London in January. He collapsed and died in hospital eight days later.
As a public meeting was held to launch the Justice for Roger Sylvester Campaign, the pressure group Inquest said relatives would visit Mr Boateng at the Home Office on 12 April.
The meeting in Hornsey, north London, was told about the family's concerns over his death and the subsequent investigation. They said reports that he was a crack addict who was behaving aggressively on the night he was restrained were not true. A Police Complaints Authority investigation, led by the Essex force, is already under way.