Interestingly, Campion is only an incidental figure in Tiger in the Smoke. It is really a novel about the anti-hero Jack Havoc, a knife-murderer following a religion he has created himself 'the science of luck'. The chilling encounter which sets the seal on this novel is not murderer-meets-detective, but when the murderer meets a clergyman who has the power to transfix him. Havoc tells the clergyman about his 'science of luck', and the clergyman tells him that he already knows this philosophy, but it is called the 'science of death'.
From here in the demise of Havoc is artistically certain. The plot accelerates, through to the final, chillingly ambiguous 'His body was never recovered.'
If you have seen Allingham as a lesser figure, after Sayers and Christie, this book should set you straight. It belongs with Conan Doyle's 'Valley of Fear' and Sayers' 'Murder must advertise' at the top of the list of British crime thrillers.