Finch was descended from a Winchelsea wine-merchant who flourished in the reign of Edward I. The family acquired Eastwell by marriage in 1560 and made it their principal residence.
Perhaps in a further attempt to protect himself from his creditors, Finch was returned to Parliament in 1614 for Great Yarmouth. He presumably owed his seat to the local connections of the Heydon family, particularly his mother-in-law, the widow of Sir Edward Clere† of Ormesby, four miles north of the borough.
