Yesterday I found the ancestry of Alice Hunt, wife of Richard Bull. They are the grandparents of Thomas Lawrence and Joan Antrobus. There's a pedigree in The Visitations Of Essex II from 1541. The pedigree mentions the Bulls, Knightons, Underhills, Caldebecks, Hinkleys, Notbeams and Pecches. Some of the connections it gets right according to David L. Greene's "The Royal Ancestry Of The Ipswich (Massachusetts) And Long Island Lawrence Families". The biggest screw ups occur with the most recent. It has Alice, daughter of a Bull of Hertford, married to Thomas Knighton of Little Bradley. According to Greene and what I've been able to confirm independently Richard Bull married Alice Hunt. Richard's parents were Charles Bull and Joan Knighton, daughter of Thomas Knighton and Anne Underhill. The pedigree gets the Knighton/Underhill connection right. The pedigree adds a Thomas Underhill and an unknown wife before Thomasine Caldebeck and Thomas Underhill. There's going back, but this gives the flavor.
The pedigree has a Richard Hunt married to Anne Knighton, daughter of Thomas. Thomas did have a daughter Anne, but she married William Mason according to Greene.
So there is a heck of a lot of work to do to try to straighten out this genealogy.