Vaughan Williams got a song called Pretty Caroline from Mrs Powell of Herefordshire (August 1908: information from the book mentioned in the previous link), and I should not be surprised if that were the one; though he also used songs found by other collectors, so the Sharp one mentioned is also a possibility; a tune comparison ought to settle it. I don't think that Mrs Powell's set has ever been published in its original form. Probably you can find more details in one of the standard works on the composer. Meanwhile, I wouldn't want to guess which of several unrelated songs which are sometimes called by that name might be in question here.

This is the second tune in the first movement, and therefore not Seventeen Come Sunday, which is the first (the third is Dives and Lazarus).