There are three explanations for the plethora of anachronisms in The Once and Future King. The straightforward one is that White's Merlyn is living through time backwards, and therefore has epistemic access to the narrative's future. These anachronisms purposely happen in the context of the story, sometimes even being called out as such as you note. Some examples of this type (which necessarily involve Merlyn in some way) are:
- Merlyn invoking Hitler to counter Wart's romantic view of war,
- the presence of the Encyclopedia Britannica in Merlyn's house, and
- when Merlyn materializes a sailor hat rather than his own wizard hat.
The second sort of anachronism is usually similar to the first in its explicitness, but comes from the narrator rather than Merlyn. The narrator tends to explain these instances as her way of making things easier on the reader, who wouldn't know the "real" medieval details. Examples of this sort include:
- discussion of the boys being sent to Eton College, which didn't exist until 1440, and
- a mention of the dessert wine port, first created in the eighteenth century.
The last category of anachronism is often more difficult to spot, and doesn't really have a precise explanation. In spite of the appearance that one can nail down the time-span of the book's action by mention of various dates (eg. when Pelinor notes that Uther died in 1216), White is purposely contradictory and fantastical with the timeline. What results is a mish-mash of features from throughout the later Middle Ages. I've pulled a few examples of this category from a Kurth Sprague essay on the topic:
- "Mordred's ambition to massacre the Jews was systematically practiced [in the late 1100's]",
- "the extravagance of dress which White describes when Arthur's court 'goes modern' [evolved in the 1300's]", and
- "The Normans .. comprise the chivalric aristocracy who .. act like fox-hunting squires of the nineteenth century."
Do note that even your typical immersive fantasy novel will tend to use anachronisms whether it likes it or not: avoiding them entirely would make the work a research project for most of us (eg. how old do you think the word 'pants' is?). So like all fantasy authors, White is using the technique in part to make the work more accessible, but there is clearly more to it than just that. Especially in The Sword in the Stone, we get a whimsical comedy in which it's almost impossible to predict what will pop up next (Robin Hood, for goodness sakes). White seems to be rebelling against the historical tone of Malory (and perhaps historical romance in general) in an effort to underscore the legendary nature of the tale. Was Uther meant to represent William the Conqueror? Did Arthur really cavort with Robin Hood? Did Merlyn actually turn Arthur into a badger? White takes all of these questions equally seriously - which is to say, not at all.
Here is a snippet from T. H. White; a biography, in which White discusses his modernistic approach (emphasis in original):
I am trying to write of an imaginary world which was imagined in the 15th century. .. I state quite explicitly that we all know that Arthur, and not Edward, was on the throne in the latter half of the 15th century, at the beginning of my second vol. .. By that deliberate statement of an untruth I make it clear to any scholar who may read the book that I am writing, as I said before, of an imaginary world imagined in the 15th cent. .. I am taking 15th cent. as a provisional forward limit (except where magic or serious humour is concerned - for instance, it is a serious comment on chivalry to make knights-errant drop their g's like huntin' men) and often darting back to the positively Gaelic past. .. Malory and I are both dreaming. We care very little for exact dates, and he says I am to tell you I am after the spirit of Morte d'Arthur (just as he was after the spirit of those sources collected) seen through the eyes of 1939. He looked through 1489 .. and got a lot of 1489 muddled up with the sources. I am looking through 1939 at 1489 itself looking backwards.