The first occurrence I have been able to find of a Sawyer is documented in “The Hidden Index of Hungerford Names” on the Hungerford Virtual Museum site. The index was compiled by Norman and Joyce Hidden, and subsequently transcribed into the linked document. On page 80 in that document we see two men:
Sagyere (Sagiere), Nicholas c1248 (Bec Custumal T/Sp3)
Sagyere, Peter le, 1246 (Monfort – Bec)
Using the reference for Nicholas I was able to find Select Documents of the English Lands of the Abbey of Bec, by Marjorie Chinball, Camden, Third Series, Volume 73, 1951. On page 68 he is listed in Hungerford Custumals. “Nicholaus le Sagyere tenet unum mesuagium pro 2s.”, which I believe translates to “…held one dwelling for 2 schillings.” The book states that this was transcribed from the original manuscript “British Museum, MS. Add. 24316“. Hungerford is on folios 36-37v. [37-38v.].
The reference for Peter isn’t so easy. There several other references in the document that are spelled differently (Montfort – Bec). There was a Simon de Montfort V who was awarded Leicester Estates in 1231. The Abbey of Bec also controlled land in Hungerford. The exact document/documents this refers to is the subject of current research.
This early spelling of Sawyer seems strange at first, but in Old English “saw (tool)” is “saga” or “sagu”. Knowing that, it’s not so strange after all.
I also have a digital copy of a land record from the UK National Archives. “Grant in frank almoin by Juliana and Clemencia, daughters of Robert son of Baldewyn le Sawere, to the abbot and convent of Battle, of land in the meadow called ‘Stokmed,’ adjoining the meadow called ‘Sandherstesmed.'” The reference id is “E 210/303” and it is dated 54 Henry III. A “grant in frank almoin” means they gave land to the church in return for prayers for their family. 54 Henry III means the 54th year of Henry III’s reign, which was 1270. The digital image is written in medieval Latin and I don’t have the background to read/translate it.