Did Dominic Grieve really say "the political neutrality of the monarch came to be accepted as “a cornerstone of the UK’s constitutional framework” "? How ignorant can you get!
Doesn't he know about Queen Victoria? She was a constitutional monarch and she was NOT politically neutral - far from it! She argued with her Prime Ministers and her Ministers for Foreign Affairs on many occasions, and even got one of them sacked. But she did recognise that the government (though nominally HER Government) ran the country and she didn't. As the article says, George V and George VI were not politically neutral either, and nor was Edward VII.
Now what about Queen Elizabeth II? She has managed to avoid political controversy in public, but surely she must express her private opinions to her Prime Minister at least once a week. She has never been a rubber stamp monarch, and I'm sure she must disagree with proposed governmental action or policy, from time to time, and I don't call that being politically neutral. The reason why she doesn't have to write letters to ministers that the public might learn about (as has happened to Charles) is that she, and she alone of the royal family, has this direct and private pipeline to the government. And of course she has had 60 years of practice in disagreeing in the most tactful manner. I don't expect she says, "Oh, no, I don't agree with X!" More likely it's more along the lines of "Have you considered Y as an alternative"?