My maternal relatives didn't serve because they were all Durham coal miners, so in a reserved occupation for both wars.
My mother was a teacher, and apparently they were prevented from joining up as well, although the mother of a friend of mine, who was also a teacher, gave up her job, and enlisted by saying she was unemployed. My mother's response to that was to wish she'd thought of that!
My father had just started an engineering apprenticeship in 1939, and he was told to finish his apprenticeship before joining - and once he'd done that, it was near the end of the war, and none of the services appeared to be interested! He had also had rheumatic fever as a child, so that may have also made the services uninterested in him.
His father is a bit of a mystery. He was in the Territorials before WW1 (5th Cheshires), and left them in 1913, but doesn't appear to have ever been called up and sent overseas (no medals), although we found a cap badge for the 22nd Cheshires when we cleared our family home a couple of years ago.