Thank you for the compliment and your offer of aid, Philip, I was just doing some more research myself, and trying to tie it all together to make it easier on you and anyone else who reads this.
I went over the Family Search records again that you came up with for Thomas Fouke born 1571, and, just going by this criteria (assuming that he WAS born in 1571), he would be the Thomas Fowke on Page 1, born about 1570, in Enborne, Berkshire. From my own research, Thomas Fowke (c1534-March 3, 1586), London merchant-of-the-staple, born to John Fowke of Gunston in Brewood, Staffordshire, and Ann Bradshaw of Windley, Derbyshire (doesn't look that far from Codnor) married Elizabeth Cupper, daughter of Walter Cupper of Enborne, Berkshire. Going by location only, it looks as though Thomas could have met her when he was a London merchant, and that their children could have been born around there. The standard listing of them is Thomas, Richard, Ann, Susan, and Elizabeth.
The most serious deviation from this listing of children is from the British History Online site that you were looking on. In an article on Acton Trussell and Bednall, father Thomas (d. 1586) has returned to Staffordshire by 1575, and purchased half of the manor of Acton Trussell and Bednall, which he leaves to his son and heir JOHN. In another British History Online article about Dunston, Thomas has also purchased the manor of Dunston in 1577, conveyed half of it, and left the other half to his eldest son and heir John, who later sells it.
This would mean that the son Thomas was not the heir, and (my hypothesis only) could have gone to Derbyshire where his cousins would have been, and perhaps wound up as a small independent landowner or tenant (I do not know what my Thomas of Codnor's occupation was). Hope this helps your generous efforts on my behalf and for anyone who looks at this, much appreciated.