Naina grew up in rural India and had withdrawn from school, left to study alone at night.
The trust’s partnership with the Aga Khan Foundation supported her to rejoin school, and she now provides training to other girls and encourages them to stay in education.
She received the Amal Clooney Woman’s Empowerment award at the ceremony.
Brandon, from Chorley, Lancashire, was given the Homesense Young Achiever Award.
He struggled with his mental health after being unemployed for a long time but the trust helped him back into work.
A Business Administration programme was the springboard for a work placement which led to a career with the same company.
Charles and Camilla switched places with Ant and Dec at the end of the night as the royals came out on stage while the TV duo were in the royal box.
The King joked: “I’ve always wondered whether someone would put Ant and Dec back in their box.”
He then thanked staff and everyone involved in the King’s Trust, adding he hoped it would go on for “as long as possible”.
The King’s Trust was founded in 1976 to help young people gain skills needed to find work.
Its courses for those aged between 11 and 30 is estimated to have assisted 1.3 million people.