After spending several months in Salt Lake City doing basic research, I have very complete information on this line.Since it will take me quite a while to get all the wills transcribed, I am providing the bare bones of Joanna's ancestry in Ahnentafel style (to find someone's father, double their number; then add 1 to the father's number to get the mother's number):
1.Joane Blake, chr. 16 Feb 1612/3, Andover, Hampshire, ENG; m/1 16 Jan 1635, Andover, (Major Gen.) Robert Sedgwick.
2.William Blake; linen draper; named in 1641 will of uncle [mother's brother] Nicholas Blake; w.d. 29 Apr 1641; bur. 13 Jun 1642, Andover, Hampshire, ENG; w.p. 18 Aug 1642, Prerogative Court of Canterbury [PCC]; m. 6 Feb 1604, Andover, Hampshire, ENG.
3.Dorothy Madgwick; w.d. 13 oct 1647; w.p. 15 Feb 1647, PCC.
4.Richard Blake; linen draper; named in 1608 will of son-in-law John Hapgood; bur. 14 Jan 1622, Andover, Hampshire, ENG; w.p. 1622, PCC.
5.Joane Blake; w.d. 23 Apr 1631; w.p. 1631, PCC.
8.William Blake of Eastontown, Andover, ENG; w.p. PCC.
9.Anne Tutt; named in will of uncle Richard Tutt.
10.William Blake of Eastontown, Andover, Hampshire, ENG.
16.William Blake; w.p. 1606, PCC
18.Thomas Tutt of Chilbolton & Wherewell, Hampshire, ENG; 3rd son; named in 1588 will of sister Winifred Poynter; named in 1589 will of Brother Robert Tutt; named in 1589 will of brother Henry Tutt; named in will of brother Richard Tutt.
32.William Blake of Eastontown & Andover, Hampshire, ENG; w.d. 20 Jul 1582; w.p. Nov 1582, PCC.
34.Robert Hibberd, tanner, of Andover, Hampshire, ENG; w.d. 16 Jun 1688; inv. 26 Apr 1589; w.p. 28 Jun 1589, Hampshire.
35.Alice ___; w.d. 31 Dec 1592; inv. 1592; w.p. 18 Apr 1593, Hampshire.
36.James Tutt of Chilboulton, Hampshire, ENG, gent., eldest son & heir; w.d. 21 Apr, 6 Edward VI; w.p. 19 May 1552, PCC.
37.Joane Waterman; sister of Christopher Waterman; w.d. 14 Apr 1556; inv. 6 Nov 1661; w.p. 13 Nov 1551, Hampshire.
72.John Tutt of Chilboulton, Hampshrie, ENG, gent; w.d. 30 Jan 1521; w.p. 1523, PCC.
73.Joane Smith/Smythe of Abingdon/Avington, Wiltshire, ENG.