Traditional Anglicanism has seen priestly absolution as declaratory, rather than judicial. Richard Hooker, the Elizabethan theologian put it:
As for the ministerial sentence of private absolution, it can be no more than a declaration what God hath done, it hath but the force of the prophet Nathan's absolution "God hath taken away thy sin", than which construction, especially of words judicial, there is not anything more vulgar.
In the prayer of Absolution in the Visitation of the Sick, the priest begins by a clear statement of the limits of his authority (according to Anglicanism). Christ left power to His Church to absolve, not all sinners, but all sinners who truly repent and believe in Him.
In the Absolution which follows the Confession at Matins and Evensong, the priest says:
Almighty God ... who ... hath given power and commandment to His ministers to declare and pronounce to His people being penitent the absolution and remission of their sins: He pardoneth and absolveth all them that truly repent and unfeignedly believe His holy gospel
Here again the minister is making a declaration that if people repent and believe then God forgives them. This may or may not be the case for any individual member of the congregation and the minister is not there to make a judicial decision as to whom it does, and to whom it does not apply. He makes a declarative statement that those who meet certain conditions are absolved by God.
If a person truly believes and truly repents, then God's forgiveness is assured, whether or not a priest declares that it is.
In the first Exhortation to Holy Communion in the Prayer Book (BCP 1662) the minister urges intending Communicants to examine themselves and to confess their sins to God with full intention to amendment of life in the future. If sins have harmed others then restitution is urged where practicable. It then goes on:
And because it is requisite that no man should come to the Holy Communion but with a full trust in God's mercy, and with a quiet conscience; therefore if there be any of you who cannot quiet his own conscience herein, but requireth further comfort or counsel, let him come to me, or some other learned and discrete Minister of God's Word, and open his grief; that by the ministry of God's holy Word he may receive the benefit of Absolution, together with ghostly counsel and advice, to the quieting of his conscience and avoiding of all scruple and doubtfulness.
The Oxford Movement in the Nineteenth Century, a key influence on the Anglo-Catholics, did not at all disagree with Article 11. They merely pointed out its limitations. Granted that justification is by faith alone, it says nothing about how such faith may be obtained, or granted, or nurtured. For some, as the Exhortation to Communion implies, priestly absolution may be an effective way of strengthening faith. In the Anglo-Catholic tradition it is seen as a sacramental grace tending to build up, or even to confer, a genuine repentance and a saving faith.
The practice of priestly Absolution, within the limits prescribed by the Church of England for its effectiveness (penitent believers) is seen as an aid to faith in those who may feel themselves to be of little faith. There is an Anglican mantra, the source of which I doo not know, regarding private confession: All may, None must and Some Should.