"You're thinking of the Great London Plague of 1664-1665, which is generally considered to have been halted by the London Fire of 1666 (though the number of infected and deaths had already begun a steep decline). The Black Death was in the 1340s."
It was still bubonic plague. There were scattered, periodic outbreaks throughout 1340 - 1666.
Here's some great reading right on point, from Mr. Kipling (who knew his onions): A Doctor of Medicine.