There are too many thats here, in my opinion, and the first one should go. "by referring to the preceding text" is an adverbial phrase modifying "It's fairly clear" and could be moved to the start of the sentence. But if you do that you get the nonsensical:
By referring to the preceding text, it's fairly clear that that it is Wavells biographical approach that is being deprecated here.
It's a natural mistake to make - there is often a "that" after "It's clear...", but if you include an adverbial phrase, then "that" should come after the adverbial phrase, and particularly should not be repeated.
(There is more latitude about where to place an adverbial phrase if you put it in parentheses/commas and clearly set it off from the rest of the sentence, but I don't really like "it's fairly clear that, by referring to the preceding text, it is Wavell's biographical approach that is being deprecated here." Because it's not Wavell's approach that is referring to the preceding text, it's the clarity of the judgment. And still one less "that".)
To take a shorter, simpler example, if you want to add "to me" instead of "by referring to the preceding text" you would write "It's clear to me that it is Wavell's approach..." not "It's clear that to me that it is Wavell's approach..."
