Though not all leaders in the CoE oppose marriage equality as currently proposed by Britain's conservative government, the church has taken an official position against it. In the article you'll read a lot of sanctimonious statements about "redefining marriage," and, as I ask in the title, isn't that the very reason the CoE exists? If England didn't have the ability to "redefine marriage" than Henry would have stayed married to Catherine and loyal to Rome.
One can also ponder, what is the Queen to do? She is sovereign of the state and head of the church. Her ministers are squabbling. Historically this would be something for a monarch to help resolve. I wonder if she will apply private pressure, which has always been Elizabeth's primary mode of operating.