Well that was clever. You want to write a British comedy of manners (with overtones of classic whodunits), and you do so via a time travel story. Truly inspired. I wish I had thought of it.
Connie Willis is an award-smothered science fiction writer (enough Nebulas and Hugos to stuff a mattress), but she has an obvious affection for those delightful old British genres. In To Say Nothing of the Dog we start in the late twenty-first century when time travel is common but really not fully controllable. A fairly influential and wealthy lady has taken it upon herself to rebuild an old cathedral that was burned during the WW2 bombing of England. She has her minions popping in and out of various points in time, getting the exact details right and trying to locate any surviving artifacts -- one in particular: the bishop's bird stump. I'm still not entirely clear on what a bird stump is, but it's an effectively silly macguffin.
In the course of all this cross-temporal scurrying about an incongruity occurs. That is to say, someone somewhere altered history in some significant way. When that happens, The Net -- the lattice of connection that is used to travel through time -- begins acting in unpredictable ways in an effort to self-correct. Time travelers don't alway end up where or when they expect to as The Net tries to guide events in such a way that the incongruity is corrected or cancelled out.
In the course of the mad search for our macguffin, an incongruity has occurred. A bad one. Soon it's all hands on deck to try to sort things out, in the course of which our hero finds himself in the middle on a bubblingly Wodehousian romp in Edwardian England to try to set things right. He is accompanied by a female colleague and together they encounter the full palette of timely characters -- the blustering aunt, the spoiled princess, the batty professor, the gruff adventurer, various young men is spats, the omnipotent butler -- as they try to piece together clues ala Poirot and, of course, fall in love.
Should you read To Say Nothing of the Dog? Yes - and that's a pretty confident yes. The story hits all the right madcap notes, but not without sly observations about fate versus free will and personality driven versus designed history. If there are criticisms they are small: it is a bit too wordy in scene setting early on, and the tangled web of causality gets quite difficult to follow, although it is well sorted out in the end. But, those are nits. It was absolutely one of the most fun books I've read in quite a while.