William was the eldest child of Thomas Rochford (Coal Miner) and his wife Ellen McNulty. He was born in Knockmore, Co. Mayo, Ireland in 1899. He had four sisters: Mary; Annie; Lizzie; and Maggie. At the time of the 1911 census, the family were living at 9 Preston Street, Rosewell, Midlothian. They had moved to Rosewell around 1910, as the census records that the youngest girl, Maggie, is the only child to have been born in Scotland.

William enlisted in1917 at Gelncorse Barracks, Midlothian. His medal index card shows that he initially joined the Royal Dublin Fusiliers (29587) before transferring to the 7th Battalion Royal Irish Regiment.

The battalion was part of the 16th (Irish) Division and was involved in action at Rosieres on 26 March 1918. During this battle, William was wounded and was taken to the casualty clearing station at Namps-au-Val, where he died from his wounds, aged 18 years.

Lance Corporal William Rochford is buried at Namps-au-Val British Cemetery. He is also commemorated on the memorial plaque in Rosewell Memorial and Church Hall, Rosewell, Midlothian.