The letter sent by Mrs Knipp to Pepys on Jan 5th could simply have been signed by her as a pseudonym " Barbary Allen" rather than her writing the song text.
Just as Pepys, in his letter of reply to her, called himself "Dapper Dicky" in answer to hers "Barbary Allen".


Jan 6th 1666
... Thence with Lord Bruncker to Greenwich by water to a great dinner and much company; Mr. Cottle and his lady and others and I went, hoping to get Mrs. Knipp to us, having wrote a letter to her in the morning, calling myself "Dapper Dicky," in answer to hers of "Barbary Allen," but could not, and am told by the boy that carried my letter, that he found her crying; but I fear she lives a sad life with that ill-natured fellow her husband: so we had a great, but I a melancholy dinner, having not her there, as I hoped.

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