The protagonist, Ned Henry, is a specialist in 20th century history, assigned to search for the Bishop's bird stump. He has made so many jumps into the 1940s so quickly that he has developed "time-lag", the time-travel-induced form of jet lag, and must recuperate before he returns to work. There is, unfortunately, an emergency in progress. A historian sent to the Victorian era has returned bringing something from Victorian England with her which the historians believe may rip time itself apart if it isn't promptly returned...and Ned, who knows virtually nothing about the 19th century, is the only one available to return it. (Theoretically, nothing may be brought through the time machine in either direction as it might cause time to unravel, and safeguards have been put in place in order to prevent significant objects making the journey.)
Unfortunately, Ned is being "prepped" on Victorian-era background information through a pair of headphones while simultaneously being told his mission and destination. As a result, he arrives in 1888 with little understanding of what he is supposed to do or where he's supposed to go other than a vague impression he's supposed to meet his contact at " Something End".
He meets Terence St. Trewes, a besotted young Oxford undergraduate, and agrees to share the cost of a hired boat for a trip on the River Thames from Oxford down to Muchings End, where Terence hopes to meet his love, Tocelyn "Tossie" Mering. Ned, Terence, Cyril the bulldog and Professor Peddick (an Oxford don) travel down the Thames navigating locks, beautiful scenery, crowds of languid boaters in no hurry to get anywhere, and the party of Jerome K. Jerome, an homage to the original novel from which To Say Nothing of the Dog draws its name and themes.
Fortunately, Ned's contact in Muchings End recognizes him when he arrives and identifies herself: she is a young woman named Verity Kindle, who is pretending to be Tossie's cousin. Lady Schrapnell sent Verity to read Tossie's diary because Tossie (an ancestor of Lady Schrapnell) had written about a life-changing event involving the bird stump at the first Coventry Cathedral (St Michael's Cathedral), an event which had caused her to elope with a mysterious "Mr. C" to America. It is only at this point that Ned learns the nature of the object he is to return: Tossie's pet cat, Princess Arjumand. (Cats are extinct in 2057 due to a feline distemper pandemic.)
However, returning the cat did not clear up the time disruption, as people attempting to visit Coventry during the air raid are still missing their target. Have they changed history by bringing Terence to Tossie? What will happen to them if Lady Schrapnell is never born? Or if Terence doesn't marry Peddick's niece, Maud, and thus doesn't become the grandfather of an RAF pilot who bombs Berlin and goads Hitler into bombing London and Coventry?
The solution involves the wisdom of Sherlock Holmes, the methods of Hercule Poirot, and the style of Lord Peter Wimsey. In the meantime, Ned, Verity and their colleagues have to deal with packs of dogs guarding the marrows, hostile theatrical costumers operating the time machine, phony spiritualists, kittens, abstruse mathematics, the Battle of Waterloo, the unalterable fact that the butler did it (they always do), the Coventry Ladies' Altar Guild, more dogs, and a crime which was committed before anyone realized it was against the law.