That they may. The problem is that the CofE is an established church, and therefore a public institution, therefore cannot be seen to discriminate. A couple in England has the lawful right to be married in their local church, so here is where the discrimination comes in. If they want to avoid this, they must disestablish the Church. Something that should have been done centuries ago, frankly.
Doesn’t the actual UK ‘gay marriage’ legislation prohibit the Anglican Church from performing ‘gay marriages?’ I thought I recalled something like that. Of course that will obviously be no barrier, I suppose, considering the the Equality legislation they have.
Freegards
It does look like not so jolly (but more and more gaye) olde Englande is dragging down that church. The two should agree to declare independence.