S/he was, beginning with Victoria as Empress of India. The last monarch so styled was George VI. You can tell this when you view the signatures of the monarchs. Elizabeth II always signed as Elizabeth R (Regina, Latin for Queen). Her father until 1948 signed as George VI RI (Rex Imperator, King [and] Emperor).
In addition, I would like to add that originally ‘emperor’ was also a legal term that implied some form of authority over all other Christian rulers (Catholics) as the heir of Rome. Legally, there could be only one heir of Rome and that position was already taken by the Holy Roman Emperor (until Napoleon) in the West and the Tsar of Russia in the East.
When Henry VIII (the many-wived Henry) split the Anglican church from the Catholic church in the 1500s, he claimed England was an empire. The Ecclesiastical Appeals Act 1532 (the Statute in Restraint of Appeals) phrased it as follows: “it is manifestly declared and expressed, that this realm of England is an empire … governed by one supreme head and king, having the dignity and royal estate of the imperial crown of the same, unto whom a body politic, compact of all sorts and degrees of people, divided in terms, and by names of spiritualty and temporalty, be bounden and ought to bear, next to God, a natural and humble obedience”. The term emperor in Europe carried with it a claim to Rome’s (or the Holy Roman Empire’s) authority. That is why France under Napoleon, Germany and Austria, as well as Russia claimed to be empires (and the Ottomans as kaisar-i-rum if I recall correctly). For Henry VIII’s England, the claim to empire meant that there ought to be no (Papal) authority above him (or the Archbishop of Canterbury).
In short, the term empire as we use it nowadays has a different meaning than the term empire used in a Christian European Context up until the 19th Cent., as a claim to universal authority over all of Christendom. Such a claim apparently did not fit British ambitions.