Originating from a Celtic source as a diminutive of Breton or Briton 

The idea here is that Brettle is taken as a diminutive of the Old French “Bret”, the name of a man who was a Breton or man from Brittany; the Bretons being originally Celts driven from Wales and South West England to North West France in the 6th century by invading Anglo-Saxons.   The Celtic knot, a symbol of the Celts, is shown here.  Some Celts returned as "Normans" much later in the army of William the Duke of Normandy who then shortly became William the Conqueror, King of England.  Many of these "Normans" then settled in East Anglia.  There were also Norman settlers in South West Scotland who were called Britons and that is another possible source;  finally it is also possible that native Welsh living in the English borders may have been referred to as “Brets” or “Brits”: so the name may come from Brittany via Norman settlements in England or Scotland or via “original Celts” from Wales!   

The authoritative work, "A Dictionary of English Surnames by P.H. Reaney and R.M. Wilson, OUP 1997" (1) suggest that the surname derives from a personal name, Old Cornish Bryttael or Old Breton Brithael but my own research suggest a concentration of Brettles and its variants in the West Midlands which is inconsistent with the origin being from Scotland, Cornwall or East Anglia where the name is less common.  However it may be consistent with a Welsh borderland origin.   Harrison (2) has Brettell as the deminutive of Brett with the present Frence forms as Bretel and later Breteau.