It was during the war of American Independence, when France and Spain made an all out attempt to recapture the Rock from the British in Gibraltar's 14th Siege, recorded as the Great Siege, which lasted from July 1779 to February 1783.

The Governor, General Elliot (later called Baron Heathfield of Gibraltar) is said to have offered a reward to anyone who could tell him how to get guns onto a projection from the precipitous northern face of the Rock known as the 'Notch'.

Sergeant Major Ince, a member of the Company of Soldier Artificers, forerunners of the Royal Engineers, suggested that this could be done by tunnelling through the Rock. Permission was granted, and Ince started work under the direction of Lieutenant J Eveliegh, a Royal Engineer, Aide de Camp to the Governor, on May 25th, 1782.

http://www.the-rock-of-gibraltar.com/Great-Siege-Tunnels/