Other people are free to also comment here but in college my British Empire history course used, "The Rise and Fall of the British Empire" by Lawrence James as an overview of the entire British empire from the American colonies to after WW2. Richard Toye's "Churchill's Empire". My professor specialized in India so we also read "The Last Mughal" and "White Mughals" by William Dalrymple. Finally, "A Hundred Horizons: The Indian Ocean in the Age of Global Empire" by Sugata Bose is a look at how the British Empire effected the countries around the Indian Ocean rim and how interconnected those countries were.