All Christians have believed in the Assumption in one form or another since the patristic age, a belief reinforced by the lack of relics of the Holy Virgin, and the veneration of the place of her repose and glorification, going back to the beginnings of church-building and public liturgies after Roman persecution. Our Lady died and was physically raised and glorified after death as a sign and promise of our own resurrection and glorification on the Last Day. Mary's Assumption is the foretaste of the assumption of the whole Church. What Jesus does for her, He will do for us.
Although the Assumption or Dormition is a consentient and universal part of ancient Tradition, it does not stand on the same level as the Trinity, the Incarnation, the Virginal Conception and Birth of Our Lord, or the Resurrection of Christ, and thus it is not acknowledged either by Anglicans or Eastern Orthodox as an essential article of the Faith and Creeds. Neither Anglicans nor Eastern Orthodox desire to dogmatise the mysteries of Our Lord's Mother. These are mysteries of love. Therefore we do not recognise the necessity of believing any version of this ancient doctrine for eternal salvation and it is not accounted a dogma, or revealed truth necessary for salvation, of the Gospel. But it is a beautiful and comforting belief which points squarely to the glory of Christ's Resurrection and its power to save all who are united to Him.
An Anglican is free to believe or not believe in Our Lady's corporeal Assumption, but all agree she died and went to Heaven! And that heaven-going, hers and ours, is what we celebrate on 15th August.