I think you're looking for Sayre Family, Lineage of Thomas Sayre, a Founder of Southampton, by Theodore Banta, The De Vinne Press, New York, 1901. It's online somewhere.
But wisely he doesn't go back beyond William Sayre who died in 1564. Researching in Podington isn’t straightforward as the pre 1658 parish register has been lost, and the BT only starts in 1602. So there are no vital events pre 1602. Other than wills, the earliest Hinwick will being the same William who died in 1564, there isn't much to go on. There's no evidence that Sayres were in Podington before about 1530.
Start with Sayre-33
I'm pretty confident that there's no connection between the Sayres of Hinwick and the Wheelers of Cranfield, despite what the unsourced profiles show.
The link between Hinwick and Leighton Buzzard is Sayre-36