There were three brothers, John, Robert, and Thomas, sons of Mary Andres Burnham and nephews pf Master Robert Andews, who were listed as passengers on the 1635 sailing of the Angel Gabriel from England to where she sank of the coast near Bristol, Maine. Passengers made it alive to Boston Harbor two days later. One of these may have been where the Canaan Burnham families descended from. More research is required.
There is a Jeremiah Burnham 1717-1760 from Essex MA, son of John, grandson of John.
Refer to Great Migrations: Passengers of the Angel Gabriel 1635 project for sources.