All the Johns agree:
But let us inquire who this Angel was? since soon afterwards he not only calls himself Jehovah, but claims the glory of the eternal and only God. Now, although this is an allowable manner of speaking, because the angels transfer to themselves the person and titles of God, when they are performing the commissions entrusted to them by him; and although it is plain from many passages, and especially from the first chapter of Zechariah, that there is one head and chief of the angels who commands the others, the ancient teachers of the Church have rightly understood that the Eternal Son of God is so called in respect to his office as Mediator, which he figuratively bore from the beginning, although he really took it upon him only at his Incarnation. And Paul sufficiently expounds this mystery to us, when he plainly asserts that Christ was the leader of his people in the Desert. (1 Corinthians 10:4.) Therefore, although at that time, properly speaking, he was not yet the messenger of his Father, still his predestinated appointment to the office even then had this effect, that he manifested himself to the patriarchs, and was known in this character. Nor, indeed, had the saints ever any communication with God except through the promised Mediator. It is not then to be wondered at, if the Eternal Word of God, of one Godhead and essence with the Father, assumed the name of “the Angel” on the ground of his future mission.
He is expressly called an “Angel” Exod. 3:2 – namely, the Angel of the covenant, the great Angel of the presence of God, in whom was the name and nature of God. And He thus appeared that the Church might know and consider who it was that was to work out their spiritual and eternal salvation, whereof that deliverance which then He would effect was a type and pledge. Aben Ezra would have the Angel mentioned verse 2, to be another from him who is called “God,” v 6: but the text will not give countenance to any such distinction, but speaks of one and the same person throughout without any alteration; and this was no other but the Son of God.
This redemption was by Jesus Christ, as is evident from this, that it was wrought by him that appeared to Moses in the bush; for that was the person that sent Moses to redeem the people. But that was Christ, as is evident, because he is called 'the angel of the LORD' (Exodus 3:2).
Given such unanimity among our reformed forebears (who themselves appealed to 'the ancient teachers of the Church') our modern reluctance to identify Him who dwells in the bush is deeply concerning. Martin Downes puts it well in a recent post:
It is somewhat ironic that the championing of progressive revelation has gone hand in hand with a diminished confidence in the revelation of Christ in the Old Testament. Historically it is as if the church has regressed and not progressed in her confidence that it was "Jesus, who saved a people out of the land of Egypt" (Jude 5, ESV).
Amen! Read his whole post here.
My sermon on Exodus 1-3 is here.