Does anyone know hòw many Christian groups believe the term 'angel of the Lord' means 'The Lord'?

Like curidusdannii stated, "almost all Trinitarians see the passages with "the angel of the Lord" is theophanies, and so visions of some kind of God himself. Amongst Trinitarians I think it would be quite rare to think otherwise."

I can also answer this question in the "negative." In other words, there are many groups that deny the angel of the Lord is the Lord. You have the Jw's, Unitarians and so-called Biblical Unitarians, Christadelphians, the mind science groups and a host of other groups.

I also noticed you quoted Judges 2:1. "Now the angel of the Lord came up from Gilgal to Bochim. And he said, "I brought you up out of Egypt and led you into the land which I have sworn to your fathers; and I said, I will never break My covenant with you."

The following is Genesis 17:7-8 where the Lord God Almighty is speaking. "And I will establish My covenant between Me and you and your descendants after you throughout their generations for an everlasting covenant, to be God to you and to your descendants after you. VS8, And I will give to you and to your descendants after you, the land of your sojournings, all the land of Canaan, for an everlasting possession; and I will be their God."

Also Exodus 20:1-2. "Then God spoke all these words, saying, Vs2, "I am the Lord your God, who brought you out of the land of Egypt, out of the house of slavery."

In short, Michael, Gabriel, or any other actual angel are not "The" angel of the Lord, the pre-incarnate Jesus Christ.

Before this question can be answered, clarification would be needed on how non-orthodox groups understand the term "the Lord". Orthodox Christianity has an ancient history of basing their understanding on the New Testament doctrine that,

"... (as indeed there are many 'gods', and many 'lords') yet for us there is but one God, the Father, from whom all things came and for whom we live; and there is but one Lord, Jesus Christ, through whom all things came and through whom we live. But not everyone knows this..." (1 Corinthians 8:6-7)

Others base their understanding of "the Lord" on a theology that has Jesus Christ previously being the archangel, Michael, who is a creature, created by God the Father. Many groups do not hold to the orthodoxly Christian faith about Christians only having one Lord - the resurrected, glorified Jesus Christ who was never created but who was with God in the beginning, who is God, and who made everything that was made (John 1:1-3). But all groups that claim Jesus Christ had a starting point in time (i.e. he is a creature - created by the Father) will have various explanations for who they view "the Lord" to be. Seventh Day Adventists, for example, would disagree with Jehovah's Witnesses at various points about who Jesus Christ is. It is usually a mistake to try to lump Seventh Day Adventists and Jehovah's Witnesses together, even though they hold some beliefs in common.

My answer to your question is simply that orthodox Christian teaching (right from the earliest times) believed what the apostles taught about who their Lord and Saviour is, as exemplified by the text I quoted above, and these ones below:

"If you confess with your mouth, 'Jesus is Lord', and believe in your heart that God raised him from the dead, you will be saved... for 'Everyone who calls on the name of the Lord will be saved' [quoting Joel 2:32 which speaks of God as the Lord]" (Romans 10:9-13).

"The god of this age has blinded the minds of unbelievers, so that they cannot see the light of the gospel of the glory of Christ, who is the image of God. For we do not preach ourselves, but Jesus Christ as Lord..." (2 Corinthians 4:4-5).

"...no-one who is speaking by the Spirit of God says, 'Jesus be cursed,' and no-one can say, 'Jesus is Lord', except by the Holy Spirit" (1 Corinthians 12:3).

The 1 Cor. text shows that there are many lords, which is why clarity must be shown in which 'lord' 'Lord' are being spoken of. The other texts show that Christians have had revealed to them by the Holy Spirit the magnitude of just who Jesus is. He's not a creature (created); he's not just a perfect, sinless man; he's not even a created angel who became a man then returned to spirit (angelic) form - and that is proven by Hebrews chapter 1. Although this Lord had spoken and appeared in some of the Old Testament accounts, often being called "the angel of the Lord" as that is how he seemed to humans on earth, it is only the New Testament that reveals the immensity of who this one is. He lowered himself to become a servant, dying as the only perfect sacrifice for sin there has ever been, and being raised in glory to be given the name that is above every name (Philippians 2:9). But those who think Jesus to be an angel (even if the Archangel), and who may be happy to call him "Lord", do not think his name is equal to the Father's name, nor do they call him 'Lord' in the sense that the Holy Spirit enables believers in Jesus to do.

That is why the term "the Lord" needs to be clarified before any answers can be given about who "the angel of the Lord" is. The "how many" aspect of the question can simply be answered by saying, "All orthodoxly Christian groups call Jesus their only Lord and Saviour in a different way to how unorthodox groups speak of Jesus." The key point is whether any group believes Jesus to have been created - or not. That is what determines their view on "the angel of the Lord". There are various groups that will equate Jesus with the archangel, Michael, and others that will say Jesus is a lord, even a god, but their definitions of those words rarely square with orthodoxly Christian ones. There's a huge semantics problem here, so if you can tighten up the meanings of the words you use in your questions, that would be helpful. Remember the first text I used: "...but not everyone knows this..." (1 Corinthians 8:6-7). To know this Lord requires the Holy Spirit to reveal him to individuals.