Is the King of England a traditionalist?

Well, Yes and No!

Certainly he thinks of himself as a traditionalist - or at any rate trad-adjacent. And he certainly self-identifies as firmly anti-"modernist".

The problem though is that if you dig a little deeper he does indeed have some very odd ideas about what modernism actually is. Yes, it's something artificial - perhaps even "rationalist" (and, at that, not necessarily particularly rational). But what is the fundamental principle of the idea? What is the source of its power?

For what it's worth, I don't think he really understands Modernism, and that's because he doesn't realise quite how deep, dark and dangerous its roots really are. And thus his "traditionalism" isn't so much anti-Modernist as simple mystical perennialism.

And that, though it may be esoteric in and of itself, is hardly a secret. As Prince of Wales, the King was a patron of The Temenos Academy, and for a time he quite literally hosted it in the headquarter of his architecture institute (which is now The Prince's Foundation).

The connexion between the King's perennialist "traditionalism" and religious traditionalism in fact comes via people like Rama P Coomaraswamy, who was one of the first generation of Catholic trads to oppose "the changes" that followed Vatican II - and who was of course the son of Ananda K Coomaraswamy, at least one of whose works is available on the Temenos Academy's website.

All of which makes it particularly disappointing that the King's own understanding of revelation is, to put it bluntly, orthodoxly Modernist.

Revelation is not deemed possible from an empirical point of view. It comes about when a person practises great humility and achieves a mastery over the ego so that ‘the knower and the known’ effectively become one. And from this union flows an understanding of ‘the mind of God’. 

[The Prince of Wales, Harmony - A New Way of Looking at Our World, p. 13]

Because this is more or less exactly point 20 (i.e. condemned proposition) in Pope Pius X's Syllabus Condemning the Errors of the Modernists:

Revelation could be nothing else than the consciousness man acquired of his revelation to God. 

[Lamentabili Sane]

My feeling, for what it's worth, is that the new King is a very nice man. But unfortunately his "traditionalism" without an actual belief in the Revelation of Jesus Christ, in person, in our human nature, on earth, via his hypostatic union with the Father, to the Apostles, and thence to His Church by word and by scripture, is not going to count for much more than a vaguely fogeyish, Scrutonian (or even Hitchensite) "small-c conservatism".