Constable on the Hill by Nicholas Rhea

The Constable Nick series starts with the constable moving, with his family, to a small village in North Yorkshire during the 1960s. It's written in a similar style to the James Herriot series - in vignettes. 

Constable on the Hill is the first of the series. Nicholas Rhea had once been a village policeman and wanted to share some of his stories. His books were made into a television series, Heartbeat, which is available on Brit Box.

Constable on the Hill is currently free on Kindle Unlimited.