Another possibility for the original Brindley is Robert, mentioned in a previous post.
From George Ormerods History of Cheshire: William Halghton, who 4 Edw. II (1310/11) confirms lands to Richard son of Robert de Brundelegh and Agnes his wife, and occurs 5 Edw. II (1311/12) in an Inquisition, when the jurors found that this vill performed but one suit to Edisbury Hundred, which the said William performed, as his ancestors had done, time out of mind.
Agnes Brindley, Richard's wife, may have been a Halghton (Haughton). So Robert was old enough to have a married son in 1310/11, he too must have been born in the 1270's.
Peter (Piers) Brindley is mentioned in 1341 along with a son, Robert, Recognizance rolls of Chester. Was this Robert named after Piers father?? A Thomas is also mentioned who may have been Piers' brother. Richard mentioned above from Ormerod may also have been a brother of Piers.
Nearly all this information is available on the internet, an advantage we have over our Brindley genealogist predecessors.