From a review of LDS indexes of parish records at familysearch.org. None of these couples is old enough to be the parents of Elizabeth Whatman who married John Brooke.
Wyllm. Whatman, b abt 1515 m abt 1540 Joan/Johan/Jone _____. Children:
1. Jane Whatman, chr 23 Feb 1541.<ref> "England Births and Christenings, 1538-1975," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/JWK7-9Y8 : accessed 07 Apr 2014), Jane Whatman, 23 Feb 1541; citing BLETCHINGLEY,SURREY,ENGLAND, reference ; FHL microfilm 97133.</ref>
2. Elizabeth Whatman, chr 9 Sep 1543<ref>"England Births and Christenings, 1538-1975," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/NRMG-1HT : accessed 07 Apr 2014), Elizabeth Whatman, 09 Sep 1543; citing BLETCHINGLEY, SURREY, ENGLAND, reference ; FHL microfilm 97133.</ref>
3. Thomas Whatman, chr 16 Jul 1647<ref>"England Births and Christenings, 1538-1975," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/NRMG-N84) accessed 07 Apr 2014), Thomas Whatman, 16 Jul 1547; citing BLETCHINGLEY, SURREY, ENGLAND, reference ; FHL microfilm 97133.</ref>
Wyllm. Whatman, b abt 1540; m abt 1565 ______. Might be the Wyllm. Whatman who married 12 Oct 1561 Cicely Homes.<ref> "England Marriages, 1538–1973 ," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/N216-4Q5 : accessed 07 Apr 2014), Wyllm. Whatman and Cicely Homes, 12 Oct 1561; citing Bletchingley, Surrey, England, reference ; FHL microfilm 307759, 97133.</ref>
Children:
1. Wyllm. Whatman, chr 27 Jan 1567.<ref> "England Births and Christenings, 1538-1975," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/NB87-33R : accessed 07 Apr 2014), Wyllm. Whatman, 27 Jan 1567; citing BLETCHINGLEY, SURREY, ENGLAND, reference ; FHL microfilm 97133.</ref> Good candidate for he who m. 19 Sep 1589 Fillis Wilamson.<ref> "England Marriages, 1538–1973 ," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/N216-Q8W : accessed 07 Apr 2014), William Whatman and Fillis Wilamson, 19 Sep 1589; citing Bletchingley,Surrey,England, reference ; FHL microfilm 307759, 97133.</ref>
2. Margret Whatman, chr 13 Aug 1570.<ref>"England Births and Christenings, 1538-1975," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/NRMG-YX9 : accessed 07 Apr 2014), Margret Whatman, 13 Aug 1570; citing BLETCHINGLEY, SURREY, ENGLAND, reference ; FHL microfilm 97133.</ref>
Thomas Whatman, b abt 1525. He is likely BROTHER of Elizabeth, and his surviving children below are likely the niece and nephew mentioned in Elizabeth Whatman Brooke's 1599 will; he m abt 1550 Ales_____. Children:
1. Elysabeth Whatman, chr 1 Nov 1552.<ref> "England Births and Christenings, 1538-1975," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/NB87-WHV : accessed 07 Apr 2014), Elysabeth Whatman, 01 Nov 1552; citing BLETCHINGLEY, SURREY, ENGLAND, reference ; FHL microfilm 97133.</ref>
2. Wyllm. Whatman, chr 5 Sep 1562.<ref> "England Births and Christenings, 1538-1975," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/J9S1-Y94 : accessed 07 Apr 2014), Wyllm. Whatman, 06 Sep 1562; citing BLETCHINGLEY, SURREY, ENGLAND, reference ; FHL microfilm 97133.</ref>
3. Benet. Whatman, chr 5 Aug 1565.<ref> "England Births and Christenings, 1538-1975," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/J9S1-TQV : accessed 07 Apr 2014), Benet. Whatman, 05 Aug 1565; citing BLETCHINGLEY,SURREY,ENGLAND, reference ; FHL microfilm 97133.</ref> Only father’s name mentioned in parish record.
Nicholas Whatman, b abt 1540; m 9 Nov 1562 Jelya. Laurence.<ref> "England Marriages, 1538–1973 ," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/N21D-BWG : accessed 07 Apr 2014), Nycholas Whatman and Jelya. Laurence, 09 Nov 1562; citing Bletchingley, Surrey, England, reference ; FHL microfilm 307759, 97133.</ref>
Nycolas Kyng, b abt 1542; m27 Nov 1567 Alys Whatman, b abt 1547. [Is she possibly a widow? wife "Ales" of Thomas, above?
I couldn't find any Bletchingley death/burial records.