We know now why Stapleton looked with disfavour upon his sister’s suitor—even when that suitor was so eligible a one as Sir Henry.
Is the reason for using a instead of an is idiomatic?
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It's because the rule is "use an before a vowel sound". Many people forget that fact. It's not about whether the word starts with a vowel or a consonant, it's whether it starts with a vowel sound or a consonant sound.
In "one" we pronounce it wʌn... the w sound is the leading sound, which is a consonant. We say "a walrus" and "a wish", so we also say "a one".