Not strictly speaking British History, but check out 100 Objects that Changed the World. It's written by the curator of The British Museum with insights from various colleagues in specialized fields. It is organized chronologically, starting with Stone Age artifacts and progressing through to the modern age. There are chapters of on average 5 pages devoted to each object with pictures and analysis of the significance of the object, what it means about the world it was created in, etc.
I listened to the 100 Objects that changed the world podcast. Great series, and well worth it. Even got to visit some of the objects in the BM last year.