Here’s the scenario. See what you can make of it.

Number 10:

‘Tony?’

The PM looked up.

‘I’m afraid,’ said Alastair Campbell, with a grimace, ‘we’re going to have to do God.’

BBC: BBC News at Six:

Huw Edwards deployed The Eyebrow to subtle effect. ‘... at Six. The Archbishop of Canterbury, the Most Reverend and Right Honourable Dr George Carey, has announced his intention to retire. Dr Carey....’

The Crown Appointments Commission:

William Chapman, the PM’s appointments secretary, shook his head. ‘The Prime Minister believes that the Church must look – and certainly an Archbishop of Canterbury, who is also, well, the centre man of the wider Communion, having a certain precedence, must look – more like modern Britain. Views are important, of course. But so are appearances, in archbishops. A certain diversity would be welcomed.’

BBC: BBC News at Six:

‘Now,’ said Huw, with an extra dollop of Welsh in his tone, ‘what is this we are hearing, Fiona?’

‘A formal announcement is expected shortly; but rumour is clamorous here at St Stephen’s Green and outside Number Ten, where Nick Robinson is standing by, that, outsider or not at the bookmakers’, the name to be sent to Her Majesty is that of –’

The (London) Gazette:

The QUEEN has been pleased to order a Congé d’Elire to pass the Great Seal of the Realm empowering the College of Canons of the Cathedral and Metropolitical Church of Christ, Canterbury, to elect an Archbishop of the See of Canterbury, the same being void by the resignation of the Most Reverend and Right Honourable George Leonard Carey, B.D., M.The, Ph.D., lately Archbishop thereof; and her Majesty has been pleased to recommend to the said College of Canons the Right Reverend Michael James Nazir-Ali, M.Litt. (Cantab), M.Litt. (Oxon), Th.D., Bishop of Rochester, to be by them elected Bishop of the said See.

Take it from there. What happens next?
 
I don't know why I didn't spot this at the time but I'll take a look at it

Well it's going to be interesting because despite your diversity point, one of the reasons I'd heard for Nazir-Ali not getting the nod, was because Number 10 and the CNC were concerned about pissing off portions of conservative Islam. There was a reason he left Pakistan you know.

But off the top of my head four things.

1: Increased dialogue and cross religious work between Christianity and Islam.

2: A lot of pissed off Anglo Catholics. While there is no fixed rule it's usually recognised that Canterbury goes Evanglical, Anglo-Catholic, Evangelic and Carey and Nazir-Ali are both Evangelicals.

3: The conservatives in the CofE and across the Communion will be very happy but the Liberals will be a little less so. The Jeffery John thing almost certainly won't happen, and women bishops may take longer than they did in OTL.

4: Hopefully more ethnic minority young people will start going forward for ordination.

The other interesting question is with ++ Michael at Canterbury will Sentamu be sent to York. Or will we get someone else like Chartres.
 
Nazir-Ali is firmly in the 'southern' or 'traditional' or 'reactionary' camp of the wordwide Anglican Communion, and would have no truck with e.g. gay rights, gay priests, gay marriage, etc. I don't remember what his position on women priests is, but I think he was firmly against women bishops.

Poor Rowan Williams had to try to build bridges between North and South (with the North American churches leading the one side and equatorial African churches the other). I suspect Nazir-Ali would plop heavily for the latter, which will do nasty things to the CofE, and tear the Communion apart.
 
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