Kensington Palace recently announced that Harry would make the fight against HIV/Aids a major focus of his charity work. He made headlines this month when he took an HIV test live on Facebook.
Harry was 12 when his mother died in a car crash in Paris in 1997. William, his elder brother, was 15. For a long time, neither spoke publicly about their grief.
But in an interview with the BBC during the barbecue, Harry urged people not to bottle up their emotions.
"It's okay to suffer but as long as you talk about it. It's not weakness. Weakness is having a problem and not recognising it and not solving that problem," he said.
During the barbecue, an apron-wearing Harry is seen flipping burgers, playing cricket and talking to sporting legends about their struggles with mental health issues.
Ferdinand, the soccer star, said Harry has "gone through different stages in his life that my kids are going to be going towards. So to get some of his experiences is very rewarding for me and very educational in many ways."
Kelly Holmes, a celebrated runner who won two Olympic gold medals for Britain, talked about suffering from depression and being able to talk about it more openly only in the past few years.
"No one knew at all what I was going through," she said.
"The key message here today is that everyone can suffer from mental health," Harry said. "Whether you're a member of the royal family, whether you're a soldier, whether you're a sports star, whether you're a team sport, individual sport, whether you're a white van driver, whether you're a mother, father, a child, it doesn't really matter. Everyone can suffer."