I'm kind of tempted to suggest 1066 and All That
, but you probably want something much more serious.
It's not a single book, but I've found various volumes in the Oxford University Press-published Very Short Introduction series to be quite good, covering many subject areas in decent but not overwhelming detail, and giving pointers to lots of further reading to follow up upon if interested. And many, if not all of their titles are available as e-books and non-Agency, so discountable with coupons at Kobo.
Here's their official series-specific site
where you can sort by category (warning, they've run the entire thing on Flash) and here's the textual US catalogue site
where you can browse by title. They've got 9 individual volumes for Britain alone, covering from Roman Britain through to the 20th Century. Their actual VSI to History is not so much a history book as a "how we look at history" book.
For a fun guide to history which covers the absolute essentials, Larry Gonick's popular "Cartoon Guide to ..." series
includes three volumes on "The Universe" and two on "The Modern World".
Off the top of my head, I'm afraid I can't really think of any single-volume non-satiric works I've personally read which fit your criteria, but likely someone else will be able to make better suggestions.
Hope this helps.