The Most Rev Justin Welby said he believes a woman will one day be made archbishop and added that some gay couples have loving relationships of "stunning quality", ahead of today's enthronement.
Pressed on the timing, he said: "Oh, I have no idea...when the right person turns up. But, yes, I think there certainly will."
In a separate interview with BBC News, the Most Rev Welby backed traditional Church teaching on homosexuality but said: "You see gay relationships that are just stunning in the quality of the relationship."
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