Final answer:
Peru is the nation among England, Australia, Canada, and Peru, that does not have English as a national language, as its official language is Spanish due to its historical background as a Spanish colony.
Step-by-step explanation:
Of the nations listed Peru is the one that does not have English as a national language. While Australia, England, and Canada have strong historical ties to the English language through the British Empire and subsequent development, Peru's official language is Spanish. In Australia, English is the primary language and is used in government, education, and media, though the country recognizes and values its diversity including the indigenous languages spoken by Aboriginal Australians.
In contrast to the United States, which has no official language at the federal level but where many states have designated English as the official language, Peru's cultural heritage and primary language is rooted in Spanish, a remnant of its history as a Spanish colony.