Educated at Stowe School and Hertford College, Oxford he joined the British Diplomatic Service in 1946 and rose to become Private Secretary to the Foreign Secretary in 1963. Subsequently he served as British Ambassador to Spain, Poland, Germany and France. He retired in 1979 but, on the election of Margaret Thatcher as Prime Minister in May of that year, she invited him to return to service as Ambassador to Washington, where he served until his retirement in 1982. It is now known that Mrs Thatcher had first asked Sir Edward Heath to take up the post, but he had refused the offer.
He was enormously popular in Washington, and he and his wife Mary formed a close personal friendship with President Ronald Reagan at a crucial time in the latter's presidency, oiling the special friendship which developed between Reagan and Margaret Thatcher.
In retirement Henderson has written several books on history, and an account of his career as a diplomat entitled Mandarin. He has also held directorships of several major British companies, including the Channel Tunnel Group, Sotheby's, and Hambros. He also has close ties with the Prince of Wales, serving as Lord Warden of the Stannaries and Chairman of the Prince's Council (the body which oversees the Duchy of Cornwall) after retiring from the Diplomatic Service. He was appointed KCVO for this service to the Crown. He gave the Romanes Lecture in Oxford in 1986.
His father was Sir Hubert Douglas Henderson, a prominent political economist and holder of the Drummond Professor of Political Economy seat at Oxford University. His mother was Faith Marion Jane Bagenal.
He was generally known as "Nico Henderson" in private life.