This is a tricky question to answer without some serious digging. The British public was, in the few accounts I found, pretty much for it. Public opinion was in many ways shaped by opium traders who had a vested interest in the steady flow. One named James Matheson started a newspaper in Britain to whip up support for aggressively-enforced free trade. I'm not sure how wide publication extended, however.

At this time (roughly 1820s-1839) the war machine gathered steam through government/commercial intelligence-gathering on the Chinese capacity for war. Government trade officials also uneasily eyed the growing trade imbalance between Europe and East Asia. There seems to be an official and cultural insistence on "progress" through expanding civilization, commerce, and prosperity. Sorry to delve into some elite/political history, there, but hey!

Trader influence: The Opium War, 2000. http://books.google.com/books?id=2W1Jmh2QpukC&pg=PA35&lpg=PA35&dq=opium+war+public+opinion&source=bl&ots=y2aurxec69&sig=xRmaDtk9dWRy8jEQGu-G9Z8ROwA&hl=en&sa=X&ei=K1uOU8GwOeTisASF-YGoBg&ved=0CCAQ6AEwAA#v=onepage&q=opium%20war%20public%20opinion&f=false

Elite and cultural attitudes toward "progress": "The Wars of the Poppies," Leslie Marchant http://www.historytoday.com/leslie-marchant/wars-poppies