I do not find Chapter 5 of In the Spirit of the Covenant terribly helpful. This first report of the Joint Implementation Commission for the Anglican Methodist Covenant, includes the chapter 'The Bread and Wine of Holy Communion'. In it, from section 5.4.12, the question of the use of the common cup in communion is raised.
As far as I can remember, the first trays of small communion cups were imported from the United States during the first decade of the twentieth century. Today the overwhelming majority of Methodist churches use them. As the report says, the reason is probably non-alcoholic communion wine, introduced around the turn of the century and fears of contacting some infection without the sterilizing effect of alcohol. It appears such an infection from a single common cup is remote, at least it was in 2005. Perhaps swine flu has raised the question again.