Several British monarchs have claimed the title of Emperor. To quote myself from an older thread on this topic:

The only time a British monarch was also titled Emperor was the period of time between 1876-1948, when the British monarchs were titled as Emperor/Empress of India. The title "emperor" in English usually refers to someone ruling over a multicultural, well, empire: a nation-state that is comprised of people of many nationalities and languages.

Queen Victoria was the first to be styled Empress, and her full style and title at her death was: "Her Majesty Victoria, by the Grace of God, of the United Kingdom of Great Britain and Ireland Queen, Defender of the Faith, Empress of India."

If you hit the link above, you can get a full table of the various titles held by the British monarchs after 1707 (when the kingdom of Great Britain was formed) and see how they changed over time.

You may be thinking "ok fine they were emperors of India, why weren't they emperors of Britain?" That's a good question, and I addressed it in this thread:

You are on the right track here -- in English, an emperor is usually someone that rules over a collection of distinct countries or ethnic groups which have united to form an imperial organization. In the case of Great Britain, the kingdom itself had overseas colonies/holdings governed from the home office, but not with full membership in the nation-state (ex: the American colonies didn't have votes in Parliament, etc.) The monarch might have personally been the ruler of those countries regardless of whether or not they were part of the nation-state of Great Britain (ex: the Hanoverian kings of both Britain and Hanover, who were legally distinct people who happened to inhabit the same body.) And there are examples of monarchs of nations that are independent of Great Britan but still have the same royal family (ex: Elizabeth II is the queen of the UK, Canada, Australia and New Zealand, as well as the Commonwealth nations, including countries that have become independent of Britain since she became queen: Jamaica, Barbados, the Bahamas, Grenada, Papua New Guinea, Solomon Islands, Tuvalu, Saint Lucia, Saint Vincent and the Grenadines, Belize, Antigua and Barbuda, and Saint Kitts and Nevis.) But there are a whole host of reasons why we call someone an emperor and not the other person, especially when translations come into play -- English is weird.

(Also, I copy-pasted the list of those countries from Wiki, I can never remember it completely.)

Anyhow, I hope that helps answer the question. Please let me know if you have other questions or follow ups!