The idea that it was a widespread strategy is a myth. Whether or not it was effective in the one instance where it is actually known to have been attempted is widely debated.

At the Siege of Fort Pitt during Pontiac's Rebellion some British did attempt to spread smallpox to rebelling natives via blankets. The idea was discussed in letters between Lord Jeffrey Amherst and Henry Bouquet, and the diary of a Captain at Fort Pitt discusses the actual giving of the blankets. Whether the Captain was ordered by Amherst or Bouquet, or came up with the idea independently or was ordered by someone else is not known for sure. Anyways the diary also establishes (obviously, since they had "infected" blankets to give) that smallpox was already in the area.

Indians did get smallpox but connecting it to the blankets is not really possible. As noted, smallpox was already in the area and could easily have been spread via contact with Europeans in battle or trade. I believe Kevin Anderson in "Crucible of War" references some natives taking smallpox infected trophies home from raids. War under Heaven: Pontiac, the Indian Nations, and the British Empire by Gregory Dowd discusses this event and is a great book. Kevin Anderson's Crucible of War also good.

The other "well known" incident of this is the US military at Fort Clark in the early 19th century. I put "well known" in scare quotes because this one was a total fabrication by Ward Churchill. The claim originated with Churchill in the 1990s and has been thoroughly debunked (sometimes by people he cited in support of his "finding").

Smallpox itself ravaged native populations, regardless of how it got there.