'Civil law' of the time consisted in whatever the king willed and was able to enforce. Must not have been a very popular 'British' concept given that the Magna Carta was signed in 1215.
And yet The Constitution of the United States of America - Fifth Amendment--Rights of Persons with the imprimatur of The Unites States Senate, gives more credit for Henry II's Assize of Clarendon of 1166 as a basis of US civil law than Becket's benefit of clergy.