The office was hereditary in the family of the Earl of Oxford (de Vere) until 1625. There were succession disputes and the last Earl died in 1703. There were various contenders and it was awarded to the son of the last earl's aunt, Lord Willoughby d'Eresby. When the heir-general and heir-male in that line failed with the death of the Duke of Ancaster in 1779, the office passed to his two daughters (the principle of co-heirs), one of whom married the Marquess of Cholmondeley, the other a Mr Burrell. The latter's part-claim to the office was then divided between her two granddaughters, who had married Lords Aveland and Carrington respectively. Up until the death of Queen Victoria, the role of hereditary Lord Great Chamberlain was exercised by Lord Aveland's son, the Earl of Ancaster.
The Marquess of Cholmondeley retains a 50% claim and therefore exercises the role in alternate reigns (William IV, Edward VII, Edward VIII, The Queen). Alternate reigns are more complicated: Victoria had Lords Willoughby d'Eresby, Aveland and Ancaster during her long reign, George VI had Lord Ancaster; George V had a Carrington in the Marquess of Lincolnshire. Precedent suggests a Carrington for the next reign (but the Aveland/Carrington 25/25% has fractured into more pieces and is becoming very complicated) and Cholmondeley once more in the reign after that.
Responses are not allowed!