I pride myself on my ability to look things up on the internet, but Google (and even AI) have been no help here....
I think the book is set in the 1940s or 1950s. It opens at the beginning of the summer holidays with the wife of a teacher (or maybe headmaster) coming home to tell him that she will not, as planned, be going away for the summer. She's excited to have the summer together. He is not. I think they're newly married? (I'm remembering her feeling like they still haven't really gotten to know each other because he's been consumed with his job since they got married).
Pretty quickly (immediately?) he disappears and she's left home alone. Their housekeeper had already started preparing the house to be empty for the summer (so I think there aren't any groceries in the house/other inconveniences).
I think at some point the local police start using the downstairs of the house as a base of operations for looking for the missing man.
Eventually it comes about that the husband (who probably turns up murdered at some point) has been having an affair with someone, and they've been meeting in a nearby cabin. His car is maybe found near the cabin at some point? Also I have a distinct memory of a picnic basket with sandwiches the trysting couple was going to eat turns up at some point with the sandwiches maybe even being moldy at some point...
Is this ringing any bells?
TIA!