Perhaps the "pipeweed" Tolkien refers to is a plant unique to Middle-Earth, albeit sharing many properties with tobacco.
Also, I am not altogether sure whether tobacco could not be grown in England. I am familiar with the climate in which tobacco is commonly grown here in the United States: areas with fairly temperate climates and warm, but not terribly hot summers. Tobacco is often grown in the Smokey (or Appalachian) mountains, so large snowfalls and/or strong rains (rain tends to get caught on the mountain-slopes) are something the plant is certainly hardy enough to handle.
EDIT: In a fantasy country, can potatoes truly be referred to as an Anachronism? If you define Middle-Earth as only referring to Europe's climate and plant life, you give us Americans, West across the Sea, an awful lot of credit.
Perhaps Tolkien decided that potatoes, in the 450 some odd years since their introduction in Europe, had become such an integral part of the culture and cuisine of the British Isles he could not separate them. Or maybe it didn't occur to him to try. Sometimes I fear we read too much into the tale...As my husband would say, "Sometimes a red car is just a red car," signifying nothing beyond the idea that perhaps Tolkien had a soft spot for fish and chips, or for tobacco.