Earlier collectors and commentators alike (Newell, Gomme, Greenaway) didn't mention its connection with the plague at all. Henry Bett, in The Games of Children: Their Origin and History (1929; Singing Tree Press, 1968), says nothing of the plague:

"There cannot be much doubt that games like Buff and Dump and Ring-a-Ring-o'-Roses, in which a laugh or a sneeze is the climax, originated in this range of quaint notions as to the uncanny significance of laughing and sneezing, and the betrayal, or the danger, or the deliverance, which these things may indicate." (p. 98)

Although Urban Legend Reference Pages: Ring Around the Rosie says "[T]he first known mention of a plague interpretation of 'Ring Around the Rosie' didn't show up until James Leasor published The Plague and the Fire in 1961," the date seems to have been earlier, because the Opies apparently had tried to debunk the theory in The Dictionary (first published in 1951). Later in 1985, they devoted a few pages to this problem in The Singing Game (Oxford, pp. 220-227):

"This story [of its being a relic of the Great Plague of 1665] has obtained such circulation in recent years it can itself be said to be epidemic. Thus the mass-circulation Radio Times, 7 June 1973, gave it a double-page headline, to advertise a documentary programme on the plague-village of Eyam (although a 1909 guide book to Eyam does not mention the rhyme); lectures at medical schools have repeated it as fact both in Britain and America (men of science are notoriously incautious when pronouncing on material in disciplines other than their own); and we ourselves have had to listen so often to this interpretation we are reluctant to go out of the house. Those infected with the belief seem unperturbed that no reference to 'Ring a Ring o' Roses' appears in Pepys's careful record of hearsay during the long months of the Plague; or that Defoe's brilliant evocation in A Journal of the Plague Year does not indicate that either sneezing or redness of spots was on men's minds at that time; or that two recent studies, Philip Ziegler's The Black Death (1969) and Professor J.F.D. Shrewsbury's History of the Bubonic Plague in the British Isles (1970), give no support to the theory, unless, that is, Thomas Vincent's observation in God's Terrible Voice in the City, 1666, is thought relevant, that roses were then neglected, since 'People dare not offer them to their noses, lest with their sweet savour that which is infectious should be attracted." (p. 221)

Their conclusion is: "Thus in 'Ring a Ring o' Roses' we have, or so it seems, a spray from the great Continental tradition of May games, that preserves the memory, however faintly, of the rose as the flower of Cupid, the wreath of roses with which Aphrodite crowned her hair, the chaplet of roses that a lover presented to his lady or with which, if she spurned him--and he followed Ovid's advice--he adorned her gatepost, the emblem that passed naturally into the social ceremony of the Middle Ages as in Chaucer's The Romaunt of the Rose...." (p. 226)

~Masato