The Duke and Duchess then spent time with individuals who have experience of the care system, including author and poet Lemn Sissay, former track and field athlete Kriss Akabusi, and writer Allan Jenkins.
Olympic medal-winning runner Mr Akabusi described how he enjoyed the stability of care, saying: "It was a saviour for me."
But he told how leaving care at the age of 16 was "very traumatic", with Kate replying: "You are petrified leaving for independence."
The Duchess asked the 400m hurdler if it had affected his relationships and Mr Akabusi replied: "Yes, but I am a loner."
He added: "Now aged 63 there is no stigma attached when I say I was brought up in care but there was a stigma when I was 16."
Mr Akabusi's parents returned to Nigeria when he was four, leaving him and his younger brother alone in the UK.
After moving around foster placements, he eventually settled in a children's home, and joined the Army after leaving at 16.