Noted for its strong unfiltered cigarettes, the brand was popular in the early 20th century, especially with army men during the First and Second World War. In the Great War, the British Army chaplain Geoffrey Studdert Kennedy MC was affectionately nicknamed "Woodbine Willie" by troops on the Western Front to whom he handed out cigarettes along with bibles and spiritual comfort.
In common parlance, the unfiltered high-tar Woodbine was one of the brands collectively known as "gaspers" until about 1950, because new smokers found their strong smoke difficult to inhale. A filtered version was launched in the United Kingdom in 1948, but was discontinued in 1988.
All sorts of advertising material carried the 'Woodbine' brand and green seemed to be the basic branding colour.
Woodbine is also another name for the honeysuckle, a widespread common climbing plant with its green foliage and potent scent on warm summers evenings.
Was the use of the word 'woodbine' for cigarettes a deliberate ploy to associate smoking with the sweeter smelling things of life? Who knows!