Hello Barbara,
I don't know if we're connected. My earliest known Mead ancestor was married in Watford, about 25 miles away towards London, in 1545. I don't know where he was born, so I've been looking at all of the Meads from around 1400 to 1650. There were a lot, especially around Stewkley, Soulbury, Whitchurch, and around Princes Risborough, Saunderton, Horsington, Bucks.
I haven't searched through all of FamilySearch, but below is some information from wills that confirms what you have for the earlier generations: Thomas / Joseph / Joseph.
From the wills, Thomas (died 1710) was married to Catherine. From other information I have, he was born in 1666, the son of Edward.
Edward was born in 1629, the son of Bennet/Benedict and Grace Hogge.
Bennet was born in 1591, the son of John.
John was born in 1557, the son of Thomas and Isabel.
Thomas Mede was an archer in the musters in 1535 and is found in the lay subsidy tax rolls in the 1540s. I have a copy of his will, dated 1569.
Thomas is probably the son of John Mede of Stewkley, who was in the muster rolls in 1522 and in the lay subsidy rolls in 1525.
Earlier there was a John Mede in the court of Common Pleas in 1484 and 1501. The earlier one is likely to be the father of the one in the 1520s, since there's a 40-year gap, though theoretically they could be the same person. The one in 1501 could be either the father or the son. As a very rough estimate, I'd say that Thomas was born around 1510, his father John in about 1480, and grandfather John in about 1450.
The earliest record I've found for them is from a Common Pleas case of debt in 1484:
1484 Michaelmas/dorses 2026
Bucks. Nicholas Funteyn, of Wynge, versus Robert Mede, of Whitechyrche, cordwainer; Thomas Kente, of Redyng, Berks, draper; John Mede, of Stuckley, husbandman. Debt.
Second entry:
http://aalt.law.uh.edu/AALT3/R3/CP40no890/bCP40no890dorses/IMG_2026.htmSince there's a Robert Mede of Whitchurch in the same entry, it's possible that Robert and John Mede are related. There were several Medes in Whitchurch at that time.
1710 DA/WE 51/168 Thomas MEAD of Stewkley, Testator
Sons Benjamin MEAD, Jonathan MEAD, Joseph MEAD, Matthew MEAD, Richard MEAD, Thomas MEAD
Daughter Elizabeth MEAD
Wife and executor Katharine MEAD
1723 DA/WF 73/192 John MEAD of Stewkley, Testator
Son William MEAD
Wife and executor Christian MEAD
1725 DA/WF 74/241 William MEADE of Stewkley, Testator
Wife and executor Elizabeth MEADE
1734 DA/WF 80/133 Catherine MEAD of Stewkley, Testator
Sons Benjamin MEAD, Jonathan MEAD, Joseph MEAD, Matthew MEAD, Richard MEAD, Thomas MEAD
Former husband Thomas MEAD
Nov 02 1734 DA/WF 80/162 Elizabeth MEAD of Stewkley, Testator
Daughter Elizabeth MEAD
Son Thomas MEAD
May 29 1760 DA/WF 94/47 Matthew MEAD of Stewkley, Testator
Brother Benjamin MEAD
1765 DA/WF 96/47 Joseph MEAD of Stewkley, Testator
Son and executor Joseph MEAD
Wife Elizabeth MEAD
1784 DA/WF 104/71 Benjamin MEAD of Stewkley, Testator
Son and executor Benjamin MEAD
Son Thomas MEAD
Grandson Matthew MEAD
1833 DA/WF 120/14 Matthew MEAD of Stewkley, Testator
Sons John MEAD, Matthew MEAD
Wife and executor Elizabeth MEAD
1840 DA/WF121/173 Matthew MEAD of Stewkley, Testator
Sons Charles MEAD, James MEAD (executor), John MEAD, Richard MEAD, William MEAD
Wife Rebekah MEAD
Granddaughter Sarah Ann MEAD