In extracts from his autobiography published in the Daily Mail, the award-winning actor/ director recalls how after their tutorials the royal wrote thanking him for helping her give an "Oscar-winning, pitch-perfect performance".
Diana - who jokingly signed herself 'the other lady in your life' out of deference to his wife - repayed the favour many times. When at one of his premieres Sir Richard told the Princess his granddaughter was upset because she'd forgotten to curtsy, Diana insisted on going back and asking the little girl for a private demonstration.
The fashionable royal also helped update her friend's image with the gift of a stylish navy Hermes tie. She instructed him to wear it whenever they met - and he poignantly wore it to her funeral rather than the traditional black one.