New Zealand came very close to implementing prohibition, and did so for similar reasons as the US (religion and a politically powerful temperance movement).

New Zealand actually had prohibition in specific provinces from its early days as a country. Then in 1911 the Temperance Movement convinced government to hold a referendum to adopt prohibition nation-wide. The 1911 poll required 60% approval to pass, so despite 55.8% of people voting in favour of the introduction of prohibition, it did not pass.

In December 1914 another vote was held, with 49% voting in favour of prohibition.

In April 1919 a third vote was held, with the required threshold set at 50%. 49.7% of people voting in favour of it - the closest New Zealand would come to nation-wide prohibition.

Further votes held in the 1920s saw a steady decline in support for prohibition.

For more information, see James Cocker and J. Malton Murray,Temperance and Prohibition in New Zealand

Canada actually had prohibition from 1918-20. However this was a wartime move to increase productivity and save resources that would be repealed in the 20s. The Faroe Islands had prohibition from 1918-1992, Iceland had prohibition from 1915-35 for wine and spirits and 1915-1989 for beer. Finland also had prohibition from 1919-1932. The temperance movement was powerful across the English speaking world as well as in the Nordic states during the 19th and Early 20th centuries