Worse than that, they are currently barred in law from those posts.
The EHRC tells us that equality for women moves at a snail's pace.
Its report says that a snail could crawl the length of the Great Wall of China in the 212 years it would take, at the current rate of progress, for women to be equally represented in our parliament.
Yet that snail would have completed well over 10 per cent of the journey since the principle of women's priesthood was first sanctioned in the Seventies (and it's fair to say our snail would have to crawl to Venus and back before we see Roman Catholic women priests, let alone bishops).
In fairness, the Church of England has begun to make some progress towards appointing women bishops.
At its General Synod in June, it voted overwhelmingly in favour of starting the legislative process to enable women's episcopacy.
But the EHRC report serves to highlight the shame and absurdity of sexual discrimination in the Church. Opponents of women bishops will claim that social issues are irrelevant to men-only bishoprics, citing scripture and tradition.
But their reading of scripture is both partial and ambiguous; they don't insist, after all, that people refrain from wearing clothes of mixed fibres and there are plenty of gospel examples of women's discipleship and apostolic mission. Once scripture and ecclesiology have fallen, it's very difficult to defend the stained-glass ceiling in women's ministry on tradition alone.
And, it must be added, social issues really are relevant. I imagine that if the EHRC report was given to churchmen of any all persuasion, they would condemn the injustice of a situation in which women are discriminated against not for reasons of talent or ability, but solely on grounds of their gender.
Justice is a big issue for the Christian churches. They lobby for it in pursuit of fair trade, in politics and on behalf of the poor and marginalised. Doubtless they would demand justice for women in their work in industry, parliament and the judiciary.
But just how seriously can they be taken in doing so, while their own top jobs are reserved exclusively for the male of the species?
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Sotto Voce
(Source: Telegraph.co.uk)