For those who are having trouble doing the research, here is some helpful info.
The papers of the Codrington family were deposited by Sir Simon Codrington at Gloucestershire Record Office in 1959 but withdrawn again in 1980 by the family and put up for sale. A campaign was launched to save the records relating to the family’s domestic estates and so they were purchased by the Gloucestershire Record Office, where they are still held as the papers of the Codrington family of Dodington, 1462 – 1940 (ref. D1610).
Original material relating to the family’s estates in the West Indies was purchased at Sotheby’s by Swiss businessman Bruce Rappaport on 15th December 1980 for £106,000, and the Gloucestershire Record Office holds microfilm copies. Other information is held in the UK by the Bodleian Library
Rappaport donated the papers to the people of Antigua and Barbuda where he was Ambassador to the Antiguan government under Lester Bird, and they are said to be held in the National Archives of Antigua.