Should Anglicans believe Queen Elizabeth II is in purgatory?

No.

The answer is definitively 'no'.

The answer is definitely 'no' because purgatory is, for historic Anglicanism, an erroneous teaching.

The question arises from a recent article on the Roman Catholic news and information website Aleteia suggesting that "Anglicanism has no binding teaching on the matter" because the Articles of Religion have no standing and that Anglicans praying for the departed Queen were affirming the doctrine of purgatory.

This, to use an appropriate phrase, is a "a fond thing, vainly invented".

While the Articles of Religion do not bind the Anglican conscience, for most Anglican provinces they remain a statement of historic doctrinal norms.  Even in The Episcopal Church, after all, the Articles are placed alongside the Definition of Chalcedon, with the note that the Articles were "established by the Bishops, the Clergy, and the Laity of the Protestant Episcopal Church in the United States of America, in Convention, on the twelfth day of September, in the Year of our Lord, 1801".  It is only slightly mischievous to suggest that placing the Articles of Religion alongside the Definition of Chalcedon - a defining statement of Christological orthodoxy - points to the importance of Article 22, 'Of Purgatory'.

The 1893 Solemn Declaration of the Anglican Church of Canada declares that with Book of Common Prayer and the Ordinal, the Articles define "the Doctrine, Sacraments, and Discipline of Christ as the Lord hath commanded in his Holy Word". Article 22, 'Of Purgatory', therefore declares "the Doctrine ... of Christ".

The Constitution of the Anglican Church of Australia states:

This Church, being derived from the Church of England, retains and approves the doctrine and principles of the Church of England embodied in the Book of Common Prayer together with the Form and Manner of Making Ordaining and Consecrating of Bishops, Priests and Deacons and in the Articles of Religion sometimes called the Thirty-nine Articles.

The Anglican Church of Australia, therefore, "retains and approves the doctrine" set forth in Article 22, 'Of Purgatory'.

According to the Declaration of Assent, the Church of England "Led by the Holy Spirit ... has borne witness to Christian truth in its historic formularies", the first of which are the Articles of Religion. Article 22, 'Of Purgatory', therefore witnesses to "Christian truth".

The Declaration of 1870 affirms "The Church of Ireland doth receive and approve The Book of the Articles of Religion, commonly called the Thirty–nine Articles", while clergy are required to make the following declaration:

I assent to the Thirty-nine Articles of Religion, and to the Book of Common Prayer, and of the Ordering of Bishops, Priests, and Deacons. I believe the doctrine of the Church of Ireland, as therein set forth, to be agreeable to the Word of God.

Article 22, 'Of Purgatory', is therefore "agreeable to the Word of God".

It is understandable, of course, why Aleteia may wish to dismiss the Articles of Religion on purgatory as irrelevant but contemporary Anglican affirmations point to a rather different context, in which the historic rejection of the teaching by Article 22 remains a normative expression of the faith received by Anglican churches.

As for the theological fantasy that was Newman's Tract XC, in which the Articles of Religion were emptied of meaning, there is perhaps no better response than that of the High Church Bishop Phillpott of Exeter, in his Charge to the Clergy of the Diocese of Exeter, 1842, with particular reference to Newman's distortion of Article 22:

Will a presbyter of our Church dare to mislead his unwary readers into a belief, that doctrine and practices, such as these, may consist with adherence to our own Articles? ... Who, then, will dare to reconcile fidelity to the Articles of our Church with adherence to this Decree of Trent?

What, however, of prayer for the departed Queen? It has been a very long-standing Anglican view that prayerful commendation of the departed is not in any way related to the doctrine of purgatory. John Donne, who preached against "their counterfeit ... purgatory", explicitly supported from the pulpit the practice of prayer for the departed, quoting from the BCP 1559 burial rite:

in respect of, and with relation to that blessed state, according to the doctrine, and practice of our church, we do pray for the dead; for the militant church upon earth, and the triumphant church in heaven, and the whole Catholic church in heaven, and earth; we do pray that God will be pleased to hasten that kingdom, that we with all others departed in tho true faith of his holy name, may have this perfect consummation, both of body and soul, in his everlasting glory, Amen.

John Cosin, in contrasting the teaching of the Roman Church with that of the Church of England, stated "we totally differ" on the teaching that "there is a purgatory after this life wherein the souls of the dead are punished and from whence they are fetched out by the prayers and offerings of the living", while yet affirming - using the same Prayer Book text as Donne - prayerful commendation of the departed:

In giving thanks to God for them that are departed out of this life in the true Faith of Christ's Catholic Church and in praying to God that they may have a joyful resurrection and a perfect consummation of bliss both in their bodies and souls in His eternal kingdom of glory.

Jeremy Taylor, who regarded the doctrine of purgatory as teaching "that the Death of Christ, his Merits and Satisfaction do not procure for us a full remission before we die, nor (as it may happen) of a long time after", noted how the patristic practice of prayer for the departed was radically different to prayers offered for those in purgatory:

For it is true, the Fathers did pray for the dead, but how? That God would shew them mercy, and hasten the resurrection, and give a blessed sentence in the great day. But then it is also to be remembered, that they made prayers, and offered for those, who by the confession of all sides, never were in Purgatory; even for the Patriarchs and Prophets, for the Apostles and Evangelists, for Martyrs and Confessors, and especially for the blessed Virgin Mary ... such general prayers for the dead as those above reckoned the Church of England never did condemn by any express Article, but left it in the middle, and by her practice declares her Faith of the Resurrection of the dead, and her interest in the Communion of Saints, and that the Saints departed are a portion of the Catholick Church, parts and members of the Body of Christ.

Prayerful commendation of the departed in the Anglican tradition has nothing whatsoever to do with the doctrine of purgatory.  This is reflected in the reserve and modesty that has traditionally accompanied Anglican prayerful commemoration of the departed, a reserve and modesty also seen in the late Queen's funeral rite.  

The opening prayer at the Queen's funeral was the collect from the BCP 1662 Burial rite:

O merciful God, the Father of our Lord Jesus Christ, who is the resurrection and the life; in whom whosoever believeth shall live, though he die; and whosoever liveth, and believeth in him, shall not die eternally; who also hath taught us (by his holy Apostle Saint Paul) not to be sorry, as men without hope, for them that sleep in him: We meekly beseech thee, O Father, to raise us from the death of sin unto the life of righteousness; that, when we shall depart this life, we may rest in him, as our hope is this our brother doth; and that, at the general Resurrection in the last day, we may be found acceptable in thy sight, and receive that blessing, which thy well-beloved Son shall then pronounce to all that love and fear thee, saying, Come, ye blessed children of my Father, receive the kingdom prepared for you from the beginning of the world: Grant this, we beseech thee, O merciful Father, through Jesus Christ, our Mediator and Redeemer. Amen.

The intention of Cranmer's composition is obvious: "them that sleep in him ... rest in him".  No purgatory awaits the faithful departed, for they rest in Christ.

The prayer at 'The Commendation' in Her late Majesty's funeral was a model of reserve and modesty: "we entrust the soul of Elizabeth, our sister here departed, to thy merciful keeping". No urgent pleading.  No petition for deliverance from purgatory. Rather, "in sure and certain hope of the Resurrection to eternal life", this was a trustful commendation of the late Queen to Almighty God until - to again quote the collect of Cranmer's Burial rite - "the general Resurrection in the last day".

Elizabeth II is not in purgatory.  The Articles of Religion of the Church of which she was Supreme Governor condemn and reject the doctrine.  Anglicans over centuries have understood that their prayerful commemoration of the departed does not at all countenance purgatory.  Her late Majesty's funeral rite, reflecting the classical Prayer Book order 'At the Burial of the Dead', was a declaration that she is now at rest in Christ.

When she is now commemorated with all the faithful departed, the idea of purgatory will - thankfully - have no place, for she is in Christ and thus at rest, for "the souls of the righteous are in the hand of God, and there shall no torment touch them".

And we also bless thy holy Name for all thy servants departed this life in thy faith and fear; beseeching thee to give us grace so to follow their good examples, that with them we may be partakers of thy heavenly kingdom: Grant this, O Father, for Jesus Christ's sake, our only Mediator and Advocate.