This is a complex question since "Britain" includes England, Scotland, Ireland and Wales. The only empire to control all of these countries was the British Empire. Other Empires controlled only parts of Britain.
The Roman Empire controlled most of Britain between AD43 and AD410, but never managed to capture the whole of Scotland, drawing the border between The River Tyne and the Solway Firth (Hadrian's Wall); the Romans also never conquered Ireland.
The next Empire to control part of Britain was the Viking confederation which invaded England in AD865. King Canute ruled over a United English Kingdom from 1016 to 1035, but after his death this Viking Empire fell apart and in 1042 the country was under the control of the Anglo-Saxon King Edward the Confessor. When he died, England suffered its next invasion by a foreign empire.
The Normans under William the Conquerer invaded Britain in 1066. They succeeded in occupying Ireland and Wales, but again never managed to controll the whole of Scotland. However they gradually became British and the final incorporation of Scotland into the British Empire occurred peacefully on 24th March 1603 when James the Fourth of Scotland ascended the English Throne as King James the First of England.
This control over the whole of Britain lasted until 1922 when the Irish Free State left the Union.
Ottoman Empire
The British Empire once controlled North America, India and Australia. Many other nations were also part of the British Empire.
At its height, the British Empire controlled 25% of the world's land surface.
The Ottoman Empire once controlled Mecca, Medina, and Jerusalem.
it once was a colony of the Kingdom of Great Britain.
At the end of WW1, the Arab lands once controlled by the Ottoman Empire came under the control of England and France.
Australia was once a colony of Great Britain.
Ottoman Empire
Britain - here you will find a developing story on Britain's role in Iraq: The Lost Library YT channel.
The Roman empire once stretched over three continents.
How were lands that were once part of the Byzantine Empire added to the Islamic world?
No one city or state has ever controlled all of Western Europe. The Roman Empire, which divided into the West Roman Empire and the East Roman Empire, came closest in antiquity, but it never controlled Central Europe or Northern Europe. The Carolingian Empire came closest in the Middle Ages, but it never controlled much of Spain or Southern Italy and never controlled any of Britain or Scandinavia. The only other state that came close was Nazi Germany, which never controlled Spain, Switzerland, Sweden, or Britain.