While my denomination (the Church of the Nazarene) does not make specific reference to the ecumenical councils in its Manual, it does state that "It receives the ecumenical creeds of the first five Christian centuries as expressions of its own faith." Thus, it expresses a continuity with its Anglican heritage, concerning the councils.
The following can be accessed on the REC's website, here.
PrefaceThe historic Anglican position maintains that no council of the Church- general or otherwise - can claim immunity from error or corruption, and indeed that all councils "may err, and sometimes have erred, even in things pertaining to God."The historic Articles of Religion of the Church of England go on to affirm that all churches and councils of the church are subject to the scrutiny of Holy Scripture, so that"besides the same ought not [the Church] to enforce any thing to be believed for necessity of salvation." (Cf. Article 21, 1662 BCP).
For these reasons, Anglicans have been manifestly reluctant to definitively enumerate those general or ecumenical councils claimed to have universal affirmation, though the first four ecumenical councils have always been held in special regard within historic Anglicanism. The following are brief summaries of the ecumenical councils of the undivided church.
Nicea I (325)Summoned by the Emperor Constantine, Nicea was the first ecumenical council of the whole Church and was summoned primarily to deal with the rise of the heresy of Arius (priest of Alexandria, d. 336) who denied the consubstantiality of God the Son with God the Father. The council condemned Arianism and defined that the Son was "begotten, not made," and thus was of the "same substance" (i.e., homo-ousion) as the Father. The crowning achievement of this council was the production of a creed which would form the basis of our "Nicene Creed." This council also fixed the date of Easter.
Constantinople I (381)This council was summoned to address a number of heresies inflicting the early Church at that time, including persistent vestiges of Arianism and semi-Arianism which suffered definitive defeat in this council's reaffirmation of the faith of Nicea (325). This council also condemned the heresies of Sabellius (who rejected the Persons of the Trinity), and Apollinarius (who denied the full humanity of Christ). But perhaps most significantly this council condemned the Macedonian heresy by clearly defining the Divinity of the Holy Spirit in the final affirmations added by this council to the creed of Nicea (i.e. the Spirit's Divine Lordship, His procession from the Father, and the equal worship and glory due to all three Persons of the Trinity).
Ephesus (431)Called by the Eastern Emperor, Theodosius II, this council condemned the heresy of Nestorius by declaring that the Virgin Mary (i.e. Theotokos - "God-bearer") bore "in the flesh...the Word of God made flesh" (i.e. incarnate). Hence the council defined the unipersonality of Christ in its affirmation of two natures (Divine and Human) cohering in one Divine Person, the second Person of the Blessed Trinity. Nestorius was thus deposed as Bishop of Constantinople. This council also affirmed the condemnation of Pelagianism (condemned at the Council of Carthage, A.D. 416), a heresy that rejected original sin and taught that man contributes to his own salvation through good works.
Chalcedon (451)The largest of the ecumenical councils, Chalcedon was summoned by Emperor Marcian to deal with the heresy of the Abbot Eutyches - Monophysitism - which claimed that there existed only "one nature" (the Divine) in Christ from the incarnation onwards, thus denying the humanity of Christ. The council reaffirmed both the Nicene Creed and the condemnation of Nestorianism by the Council of Ephesus, and in its own Definition (largely based on the famous Tome of Leo the Great), declared the final word on the Hypostatic Union of the Divine and Human natures of Christ, being fully God and fully Man with no diminution or commingling of either nature. Chalcedon represents the definitive victory over the Christological heresies plaguing the early Church.
Constantinople II (553), Constantinople III (681), Nicea II (787)Anglicans generally acknowledge the fifth and sixth ecumenical councils (both held in Constantinople) to be consistent with, though adding nothing to, the substance of dogma defined by the first four councils. Largely disciplinary in character, Constantinople II (553) condemned a collection of writings allegedly supporting Nestorianism known as the "Three Chapters," while at the same time the council upheld the Definition of Chalcedon. Constantinople III (681) condemned the heresy of the Monothelitism, a contrived Christological model intended to appease the Monophysites by attributing only one will or operation to Christ (the Divine), instead of two (Divine and Human). Nicea II (787), the so-called seventh ecumenical council, is disputed in respect of its ecumenicity and application, though in principle its condemnation of Iconoclasm is conceded to be orthodox.
From Appendix A of the Reformed Episcopal Constitution & Canons (2005)