The brothers were reservist John (37), soldier Patrick (36), infantryman James (33), infantryman William (32), infantryman Martin (29), infantryman Thomas (27), infantryman Arthur (24), gunner Henry (22), sailor Ernest (21) and sailor David (18).
The family's only fatality was the eldest, John, who was gassed in the trenches in France and died in 1916 after being transferred back to a UK hospital.
His grave, in a remote area of a cemetery in York, is the only place where any of the men's service is commemorated.
The grandson of Ernest Calpin, 68-year-old Michael, is calling for a permanent memorial to be erected, amid fears that their place in history will fade into obscurity.
“Their achievement has gone unrecognised, it would just be nice to have a civic-type plaque in honour of the sacrifice they made.
“When they came back from the war they were just completely forgotten.
"For 10 brothers to actually sign up is a unique thing which will never happen again.”