The king and queen stayed the king and queen, why didn't they change to the emperor and empress?
The British monarchs were titled Emperor/Empress between 1876 and 1948, between the time Victoria assumed the title Empress of India and when India gained its independence and George VI dropped it from his title/styles. Here's a handy chart I made for an older comment; I should explain that these date from the Act of Union of 1707 which created the political entity of "Great Britain."
| Years | Style | Monarch |
|---|---|---|
| 1707–1714 | By the Grace of God, Queen of Great Britain, France and Ireland, Defender of the Faith, etc. | Anne |
| 1714–1801 | By the Grace of God, King of Great Britain, France and Ireland, Defender of the Faith, Archtreasurer and Prince-Elector of the Holy Roman Empire, Duke of Brunswick-Luneburg | George I, George II, George III |
| 1801–1814 | By the Grace of God, of the United Kingdom of Great Britain and Ireland King, Defender of the Faith, Arch-treasurer and Prince-Elector of the Holy Roman Empire, Duke of Brunswick-Luneburg | George III |
| 1814–1837 | By the Grace of God, of the United Kingdom of Great Britain and Ireland King, Defender of the Faith, King of Hanover, Duke of Brunswick | George III, George IV, William IV |
| 1837–1876 | By the Grace of God, of the United Kingdom of Great Britain and Ireland Queen, Defender of the Faith | Victoria |
| 1876–1901 | By the Grace of God, of the United Kingdom of Great Britain and Ireland Queen, Defender of the Faith, Empress of India | Victoria |
| 1901–1927 | By the Grace of God, of the United Kingdom of Great Britain and Ireland and of the British Dominions beyond the Seas King, Defender of the Faith, Emperor of India | Edward VII, George V |
| 1927–1948 | By the Grace of God, of Great Britain, Ireland and the British Dominions beyond the Seas King, Defender of the Faith, Emperor of India | George V, Edward VIII, George VI |
| 1948–1952 | By the Grace of God, of Great Britain, Ireland and the British Dominions beyond the Seas King, Defender of the Faith | George VI |
| 1952–1953 | By the Grace of God, of Great Britain, Ireland and the British Dominions beyond the Seas Queen, Defender of the Faith | Elizabeth II (before coronation) |
| From 1953 | By the Grace of God, of the United Kingdom of Great Britain and Northern Ireland and of Her other Realms and Territories Queen, Head of the Commonwealth, Defender of the Faith | Elizabeth II |
As /u/jschooltiger states, but also it's worth highlighting additionally that whilst the monarch held the title of emperor or empress regarding India, this was an additional title to the one they already held as King or Queen of Great Britain. Aristocrats hold multiple titles - it is possible for a title to be promoted, but generally titles are simply accumulated. The UK is a kingdom, and the title of its ruler must be King or Queen. Generally when an aristocrat gains a more senior rank, this becomes their primary title, and lower titles are often given to sons as 'courtesy titles' that have no legal meaning. The case of the British monarch in this instance is thus interesting, as an emperor is more senior to a king, but because India was a territory under Britain, the title of King of Great Britain etc retained seniority. It's worth pointing out at this point that although it seems like a rigid system with complicated rules, titles and nobility actually flexed and even broke in order to meet the political use required of them - in this case to reinforce the idea of British primacy amongst the European powers, and consolidate its establishment of official sovereignty in India.