The article below discusses the whole thorny question. Certainly at the time any children of the marriage, being considered illegitimate under British law, wouldn't be in the line of Succession. This article also states that the marriage was the only time that permission to marry was withheld by a British monarch after a formal request.
https://en.m.wikipedia.org/wiki/Princess_Sophie_of_Greece_and_Denmark
The most frequent disqualification actually came not from a refusal to consent (which, as you said, only formally happened once), but rather from people not actually asking for consent (possibly because they knew it would have been withheld, or because they didn't care, or because they didn't even know they had to).
The interesting thing, as I said above, is that the 2013 Act retroactively legitimized all the descendants from those unconsented marriages, but, for the purposes of the succession to the Crown specifically, they are treated as if they were still considered illegitimate.
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