England joined the First World War because _____.

The German government wrote to the Belgian government on August 2, 1914, the day before Germany declared war on France, requesting the right of free passage via Belgium for its troops so that they might most effectively invade France and reach Paris.
As Belgium refused to allow passage, Germany and France went to war on August 3rd. The following day, France invaded Belgium, which prompted Britain to join the conflict to protect Belgian neutrality.