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Mr. Hague said that Britain represents 12 percent of the bloc’s population, but Britons make up only 1.8 percent of its staff. “It is mystifying to us that the previous government failed to give due weight to the exercise of British influence in the European Union,” he said.

The diplomatic chief also identified Indonesia, South Africa, Kenya and Nigeria as countries and all of Latin America as places where links need to be strengthened.

Mr. Hague said Turkey’s Foreign Minister Ahmet Davutoglu will visit Britain next week as London seeks to upgrade ties to Ankara. Turkey “is a good example of a country developing a new role and new links for itself,” he said.