Are the Conservatives starting the break-up of the United Kingdom?

It sounds like it. Conservative MP Alan Duncan says:

"I'm beginning to think it is almost impossible now to have a Scottish prime minister because they would be at odds with the basic construction of the British constitution,"

..because of the so-called West Lothian question, which has been around in one form or another since the Irish Home rule debate in 1886.

So the Prime Minister of the United Kingdom cannot come from Scotland. Hum...I imagine dolls of Mr Duncan being sewn together by eager seamstresses in Auchtermuchty as we speak, while Jock and his mates sharpen up the pins. (With acknowledgements to the late Sir John Junor)

If that argument applies to a Scottish prime minister, it also applies to a Northern Irish prime minister or a Welsh Prime Minister because of the assemblies which cover (or should cover, in the case of Northern Ireland) those areas.

So, the Prime Minister of the United Kingdom can only be English, if you follow Duncan's logic.

Brilliant. How to destroy the United Kingdom in one easy lesson, and, by the way, ensure that the current dearth of Tory MPs in Scotland continues for a long while.

Of course, the Tories would never, even under extensive torture, admit that the solution to this problem is to have a proper English Assembly or proper directly-elected English regional assemblies. That solution would still retain a United Kingdom parliament and the Prime Minister could fairly come from anywhere in the United Kingdom including Penzance, Lerwick, St Davids or Enniskillen.