SS GB by Len Dieghton
Whilst not a war book per say, it is set in England in 1941 and involves an Inspector from Scotland Yard investigating a murder.
The thing is, this is an England under Nazi occupation, a defeated England making do under the boot of Nazi conquest.
The crime story begins as any other might, but quickly becomes the focus of Resistance activities, plots, and the machinations of those within the German military and government, and foreign powers. Scotland Yard Detective Superintendent Douglas Archer finds what was a simple murder turning into a juggling act between himself and numerous powerful groups.
What really sets this book apart is Deighton's sweating the details of a Britain conquered. We are used to England as a special case of World War II in Europe, the country untainted by Nazi occupation, a somehow nobler land of heroic resistance. Deighton sets this on its head, makes England a Vichy regime, and raises the issues of occupation and collaboration in an unexpected place. The world of SS-GB is a mere twist away from what might have been. The transplant of the troops of occupied France to England is a fascinating exercise in playing with our entrenched picture of Britain At War, and allows a (perhaps small) reevaluation of the collaborationist governments of 1940's Europe.
A fantastic "What-if" and it would be a great companion piece to Fatherland by Robert Harris. (Another what-if involving a SIPO officer investigating a murder in 1964 in Berlin in a world where Germany won the war)