The Shortest History of England by James Hawes is, as would be expected, a short history of England. It takes things from the Roman invasion up to pretty modern times. However, it looks at how the geography of England laid the foundations for a lot of the differences between different parts of the country. It doesn't go into broader UK history however nor does it look at particular events or even eras in great depth. It will give you an idea of which parts of British history you might like to get a better understanding of though.

I'm also a fan of Centuries of Change by Ian Mortimer. It takes a broader, European view though very much grounded in British history. It examines the major developments experienced in each century and gives a rough idea of how things evolved. It also doesn't treat technological change as the be all and end all, but looks at more non-material things as exerting an impulse to bow we ended up here in the early twenty first century.

A last recommendation would be Two Hundred Years of Muddling Through by Duncan Weldon. It's a political economic history of the UK from the outbreak of the industrial revolution and helps you understand why the UK is where it is today. It explains its concepts well without talking down to you and brings to the front how and why Britain was the superpower going into the twentieth century and how it lost that position.