How Many Countries Were in the British Empire at Its Peak?

At its territorial zenith (early 20th century, post-WWI), the British Empire comprised approximately 56 countries plus numerous colonies, protectorates, mandates, and dominions.

It was the largest empire in history, covering ~13.7 million sq mi (35.5 million km²) – about 24% of Earth's land area – and governing ~412 million people (1913).