Joseph was born on 10 May 1916 in Mile End Old Town, London to Richard Cohen and Frances nee Garcia and he had two sisters, Jenny and Sadie and a brother Martin. In 1933 Joseph officially changed his surname from Cohen to Garcia-Webb when he applied for a position working for the civil service. He married Miriam Beitler in 1939 and they were listed as living at 48 Claremont Road, West Ham where Joseph worked as a general manager. They had two children, Diane born in 1940 and Peter born in 1942.

Joseph enlisted in 1940 and trained as a pilot. He was the pilot of Mosquito ML907 which departed from RAF Little Staughton on a daylight operation at 13.45 to take part in Operation Jülich. A series of bombing raids on three German towns, Düren, Jülich and Heinsburg to support the US first and ninth armies in the area between Aachen and the Rhine. On the return to base they encountered very poor visibility and on nearing the runway the aircraft was seen to pull up sharply to avoid high tension cables. The aircraft stalled and spun near the airfield killing both Joseph and his navigator Robert John Wendes, 1380740