The United Grand Lodge of England was formed in 1813 through the union of the Grand Lodge of England and Westminster (“Moderns”) and the Antient Grand Lodge of England (“Antients”). For the coat of arms, inspiration was obviously taken from the coat of arms of the “Antients“, not of that of the “Moderns“.
I have not yet found out if this coat of arms (or an earlier version) came in use immediately in 1813.