When asked whether the King would be feeling "pressure" over the allegations, Dimbleby said: "I think that he will be feeling the pain of this" and be "appalled by the allegations".
Dimbleby added that Charles would be "sensing the need to give duty of care" to Mountbatten-Windsor, describing Andrew as "a broken, finished man at best".
Last week, Buckingham Palace said it was ready to support the police as they consider allegations against Mountbatten-Windsor. Mountbatten-Windsor has consistently and strenuously denied any wrongdoing.