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 Conqueror and many of those 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" 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. 

 More detailed information, from which the comments above were derived can be found here which lists the first use of the name by Godwin Brytael in 1035 under the reign of King Canute, with a later record of a Reginald Bretel in the Pipe Rolls of Huntingdonshire, dated 1169.  The Oxford Dictionary of Family Names also mentions Godwin Brytael and lists Brithael as an Old Breton personal name adopted into English usage before the Norman conquest to then become the Middle English Bretel, Britel and Brutel.  A similar derivation  is shown below .

From the Old Breton male personal name Brithael. It was adopted into English usage before the Conquest becoming Middle English Bretel Britel and Brutel. Compare Godwine Brytæl 1035 in Tengvik (Dorset).alternatively in some instances from the Middle English personal name *Bretel or *Bertel an unrecorded survival of Old English Beorhtel. alternative pronunciation of Bridle or perhaps Britwell . Some of the post-medieval bearers cited under (1) may belong here.

Source: The Oxford Dictionary of Family Names in Britain and Ireland, 2016

Similar surnames: Fretwell, Britnell, Kettell, Trettel, Bethell, Brett, Bottrell