John Dickson Carr (who also wrote under the name of Carter Dickson, although many reprints use the Carr name) was an American who spent most of his adult life in England. He is the classic equivalent to Agatha Christie in fair-play whodunit puzzlers. He’s also the all-time world champ in locked room and impossible crimes. As Carr he wrote about Gideon Fell; as Dickson he wrote about Sir Henry Merrivale. Both have a dose of humor but the Merrivale books also have a dose of farce.
Anthony Berkeley Cox also wrote under two names. “Francis Iles” wrote classic “inverted” mysteries, in which you are shown the murder and then are lead to wonder how - or if - the murderer will be caught; deep psychological mysteries for the day. His “Anthony Berkeley” books about detective Roger Sheringham are more classic whodunits.
Leo Bruce wrote Case for Three Detectives in 1936, a parody involving Father Brown, Hercule Poirot, and Lord Peter Wimsey failing to solve a locked room mystery that his own stolid lower-class Sergeant Beef solves with ease. I’ve never gotten into the rest of his books but he wrote many.
Poet C. Day-Lewis wrote the Nigel Strangeways whodunits under the name of Nicholas Blake. Erudite, witty, and well-written, they are also a bit too steeped in British comedy of manners parody for my tastes but they are good books and someone from England would probably appreciate the fine points more.
Peter Dickinson didn’t start writing until he turned 40 and then three of his first five mysteries were among the best ever. (The Glass-Sided Ants Nest, The Old English Peep Show, and The Poison Oracle, although the UK versions have alternate titles.) Although these books had a policeman hero, they were nothing like what anybody else was writing, a complete revitalization of the field. He’s continued to write brilliantly for the last 35 years.
In the “nobody-else-in-the-world-writes-like-him” category is William Marshall’s series of Yellowthread Street police procedurals set in British Hong Kong. More farce than Dickson, more psychology than Iles, more sheer weirdness than Dickinson, he’s unique. You will either devour him or hate him.