Theological disputes within the Church of England are emphatically not a matter for me; however, if I may be forgiven a nit-picking academic/legal technical point, the views in the passage quoted from the Jesmond Conference paper seem to rest on a category mistake, confusing the nature and role of the Church of England with the issue of legal personality. The former is (presumably) about its theology, mission and ministry: the latter is about its lack of capacity to bring legal proceedings and nothing more.
Nor is it alone in that lack of capacity. The Church of Scotland is not generally regarded as having legal capacity qua Church of Scotland: an action would be raised either by the General Trustees or by one of the Boards or Councils of the Kirk, as appropriate to the issue: see, for example, Percy v Church of Scotland Board of National Mission  UKHL 73. Similarly, in an action involving British Methodism, the claimant or defendant would be the President of the Methodist Conference, not “The Methodist Church”: see, for example, President of the Methodist Conference v Preston  UKSC 29.