The way in which the United Kingdom was previously divided into tribes/kingdoms, and how these were impacted by invading nations (it helps give some context for place and family names, language, and the differences between areas now).
How Britain's wealth was created: agriculture, industry, slavery, colonialism, natural assets (helps to understand why we became so powerful). And the impact that those things had on the nations we ruled.
Our history of warfare (our history of allegiances and enemies help us to understand that we have no "natural" friends or enemies in the world).
The history of the two world wars (help us understand the danger of unfettered and unchecked nationalism, the way the media can manipulate people's views, the disastrous consequences of excessively punishing nations financially, and the benefits of mutual cooperation. It would also help us to break down the myth of the Blitz Spirit, and that just because someone is good at ruling during wartime, does not make them a perfect person, and does not excuse their actions in peacetime).
The retreat from empire, and our position in the world; how colonialism has shaped our relationships with other nations (in a variety of ways). The European Union, and its impact on stability and prosperity within Europe.
Our political system, and how it works. The basis for our laws, and the importance of political neutrality in our institutions.
The history of religion, and how the break from Rome impacted our society.