On page 35 of the aforementioned book Mayhew discusses the common law in the context of its religious component. Mayhew does NOT want (obviously speaking) Anglicanism incorporated in the common law, even though Anglicanism was part and parcel of "the law of England."
Claims about Christianity and the common law abound. One claim is that the common law is derived from Christianity and that claim is clearly false. As Mayhew accurately notes (as Jefferson would later -- this was published in 1764) the common law had its origin in heathen nations and was a "complete" system long before the reformation. JM's opponent attempted to argue that the Anglican establishment was smuggled into the American colonies via the common law-law of England or whatever de jure/de facto system of British rule that controlled in the colonies at that time.
It will not, I conclude, be asserted, that all the laws of England, without exception, or of Great Britain, are, as such, binding on the colonies. In order to their being so, it must, I humbly conceive, plainly appear from the language of them, or from their very nature, that they were formally designed for all the King's subjects, as well those in the colonies as those in England. Many of the laws of England are in their own nature local, so that they cannot possibly be obeyed out of England. And I am informed by those that are learned in the laws, and in the customs and usages of the colonies, that it is a clear, indisputable point, that there are many English statutes, in other cases, which are not binding on the colonies. So that jt seems to be only the common law at most, and those statutes that are made in affirmation or explanation of it, that English subjects carry with them when they emigrate, emigrate into colonies, so as to be bound by them. And I conclude, it will not be said that the church of England is established by common law, which had its origin among heathen nations; and was compleat as a system long before the reformation.
Whether common law that is pagan in its origin later incorporated Christianity is a more difficult question.