Bangladesh, March 1 -- “First they ignore you. Then they ridicule you. Then they attack you and want to burn you. Then they build monuments to you.” These words, spoken more than a century ago by trade union organiser Nicholas Klein at a Baltimore garment workers conference, seem to capture perfectly the political moment facing the Green Party in the United Kingdom today. After years of relative obscurity, the Greens are moving from the “ignored” to the “ridiculed” phase-and the next stage, Klein warned, is always the hardest.

For much of the last decade, the Green Party existed on the margins of British politics, often dismissed as idealistic but ultimately inconsequential. Even when their policies ad...