Coton House was once the home of the Dixwell family. Edward Dixwell lived there at the beginning of the 17th Century - his youngest son John (1607-1689) was a Member of Parliament; a judge in the trial of Charles I and a signatory of the King's death warrant.
We don't know how much time John spent in the house near Rugby, but it is believed that he was brought up in Kent by his uncle, Sir Basil Dixwell of Brome. In 1646 he was elected as the MP for Dover.
The trial of Charles I was held in Westminster Hall. A description of the trial can be found at http://history.hanover.edu/courses/excerpts/212trial.html. It is claimed that the death warrant was signed in a room in the cloisters of St Stephens, where one of the offices of the Parliamentary Labour Party now stands. [Fiona Gordon, the Prime Minister's Political Secretary had her office in the room when Director of Political Services and Secretary of the PLP].
John Dixwell's signature is the last but one in the fifth column on the death warrant - a facsimile of which is currently on display in the Robing Room of the Palace of Westminster.
When the monarchy was restored in 1660 Dixwell fled to Prussia. It was a wise move - the 'regicides' who had died had their bodies dug up and abused; 24 ended up in royal dungeons, some being executed in particularly unpleasant ways - while just a dozen escaped. Little is known of Dixwell until he turned up five years later in New England. He settled eventually in New Haven, Connecticut - where he took the name 'James [sometimes 'John'] Davids', some knew him just as 'JD' and he described himself as a retired merchant. It was only on his deathbed that his true identity was revealed.
Dixwell died on 18th March 1689 and was buried on the New Haven Green between the (Center) church and the site of what is today, Yale University.