Anglican Mainstream leaders wrote this letter to the House of Bishops of the CofE. And another one, apparently on 3 October. Anyway, they got a reply from the secretary of the HoB, which they have published. It can be read here. It should be read in full, but does contain the following key paragraphs:
In relation to the church’s room for manoeuvre in relation to the law there were two separate issues. The first is whether it would have been legally possible for the Church to have made registering a civil partnership incompatible with being in Holy Orders. The second concerns the changes to various references to ‘spouse’ in church legislation (for example on pensions).
On the first, the answer is that there will no doubt be denominations or faith groups who will regard being in a civil partnership as intrinsically incompatible with membership of their ordained ministries. That is the position of the Roman Catholic Church. The law does not preclude that approach where the prohibition is based on doctrine or religious conviction. For the reasons set out above, however, civil partnerships do not necessarily involve activity contrary to the teaching of the Church of England (as contained, for example, in the 1987 Synod motion). The bishops did not, therefore think it warranted to seek to impose a prohibition.