Can anyone help me identify this novel.

It was written by a British author and set in a small provincial British
town, possibly in the 1960s. A man (possibly a drug dealer - certainly an
undesirable character) has been found murdered in a park. The detective in
charge of the investigation eventually begins to suspect that his own son
was the murderer and privately uncovers evidence that proves it. When
challenged, the son confesses to his dad. But because he secretly condones
the murder and because he is dying of cancer and will soon leave the job,
either by early retirement or by dying in the job, the detective agrees to
take the blame, confident that his boss will hush things up because he too
thinks the man deserved to die.

The detective dies soon after taking early retirement on medical grounds.
The chief constable keeps his secret. The son is never punished for the
murder.