Just one important fact is misrepresented in Judith Flanders's book - namely the consequence of John Wesley's decision that he himself should "ordain" ministers for the new non-conformist movement that he had developed since the 1730s.
He was an Anglican priest but he had never been consecrated as a bishop, and therefore simply could not ordain priests himself. So after he started acting in this episcopal way, the total breach between Methodism of whatever variety and the established church in England and Wales was firmly and irrevocably plain.
This breach was further defined by the Methodist decision not to use wine but un-fermented grape juice in Methodist communion services. Ironically, of course, Wesley himself was a High churchman who put a refreshed importance into the practices of fasting, preaching, and conversion. However, the book is completely wrong when it implies that Methodism remained part of the established Church of England after the 1780s, since it most certainly did not.
And a serious attempt to reunite Methodism and Anglicanism in the 1970s and 1980s foundered on precisely the Anglican requirement that Methodist ministers should undergo some form of formal re-ordination (during a ceremony of reunion at which both churches would in a way "recognize" each other's orders) implying that the Methodist ministry was to an extent defective and imposing an unacceptable requirement for Methodism.
The same, of course, would probably be needed if Anglicanism were being reconciled with the Holy See.