The time is England in the age of Napoleon. There are societies of magicians in England, but it turns out none of these magicians is actually capable of performing magic. They write articles, debate and hold meetings, but in all of England no one can cast a simple spell. We learn that this is different from England's past, which had abundant magic users. (I am not sure how Clarke's England can have a magic-rich past, different from our own history, and yet end up in the Napoleonic era with everything in common with our history.) A man named Mister Norrell approaches the magician society of York, and offers to demonstrate a feat of magic. If he can indeed perform magic, then the society members will acknowledge that they are frauds, and they shall "practice" magic no more. The society agrees, and meets in York's cathedral at the time Norrell specifies. I really liked the scene that followed, it is one of the best in the book.
Norrell has proved he is a real magician, but he is not taken seriously by the government of England. He moves to London, and commits a second act of magic, which DOES draws the attention of the English lords, but it also sets in motion the rest novel. It is an age old tale - man's folly in dealing with power beyond his control - but it is worth reading anyway. There are consequences for actions, though they are not immediately apparent to the characters in the novel. The reader, of course, can see the devastating effects upon some of the well drawn characters in this book, especially well done is the plight of the honorable butler.
Eventually, a second man appears in England who has the gift of magic. This is the younger, and more likable, Jonathan Strange. He arrives in London to become Norrell's apprentice. (Norrell is notoriously jealous of his craft, hoarding all the books on spell craft and attempting to crush any threat to his exclusive position as chief magician in England.) The personalities of Strange and Norrell are different, and of course this leads to conflict. Strange is all for spreading magic to everyone, while Norrell wants to keep all the knowledge to himself. I never did quite understand why in all the world only Strange and Norrell seem to have these magician powers. Why not, for example, a French magician to battle at Napoleon's side against Wellington and Strange?
The world of fairie is also described. It is magicial place, but not a nice place. In fact, it can be quite dangerous, and this adds some of the spice to the latter half of the novel.
I think this book is deliberately written in the style of last century English authors. But since I haven't read, Dickens, I can't be sure. There are footnotes in the text, giving background information to the reader. There is lots of character talk but not of drama - no sorcerous battles or swordplay or chase and escape adventure. It makes for interesting reading, but I bet the movie version jazzes up some of the plot points.