In March 1918, the Germans began their Spring Offensive and the 19th Battalion, as part of the 2nd Division, helped in shoring up the front-lines as the Germans advanced. On 7 April 1918, while holding the lines near Villers-Bretonneux, his company, with Storkey as its second-in-command, was sent forward to clear Hangard Wood, believed to be lightly held by the enemy. The company commenced its advance early in the morning after a covering artillery barrage lifted, but Storkey had fallen asleep and was left behind at the starting line. He shortly woke and quickly caught up with the advance, about 70 metres (77 yd) ahead. By this time, machine gun fire had caused a quarter of the company to become casualties, including its commander, Captain Clarrie Wallach. Taking command, Storkey led a small party on a foray to outflank the machine gun post that was holding up the advance. Despite being detected as they approached, he seized the initiative and led a prompt charge that saw his party capture a machine gun along with 50 Germans and killing or wounding about 30 more. His conduct leading the attack had deceived the Germans into believing the size of the force facing them was much larger than it was.
The position secured, the Australians pushed on further into the wood but were unable to locate their objective. Storkey, considering the available options for cover too exposed, opted to withdraw the company back to their starting positions. On reporting to his battalion commander, he was ordered to retake the position but advised that he had too few men to so. His explanation was accepted and Storkey returned to his trench. Over 150 soldiers of the company had become casualties of the attack, but it had resulted in useful information on the German forces at Hangard Wood.
For his actions at Hangard Wood, he was awarded the Victoria Cross (VC). At the time, the VC, instituted in 1856, was the highest gallantry award that could be bestowed on a soldier of the British Empire. The citation for Storkey's VC, published in the London Gazette, read:
For most conspicuous bravery, leadership and devotion to duty when in charge of a platoon in attack. On emerging from the wood the enemy trench line was encountered and Lt. Storkey found himself with six men. While continuing his move forward a large enemy party—about 80 to 100 strong—armed with several machine guns was noticed to be holding up the advance of the troops on the right. Lt. Storkey immediately decided to attack this party from the flank and rear, and while moving forward in the attack was joined by Lt. Lipscomb and four men. Under the leadership of Lt. Storkey, this small party of two officers and ten other ranks charged the enemy position with fixed bayonets, driving the enemy out, killing and wounding about thirty, and capturing three officers and fifty men, also one machine gun. The splendid courage shown by this officer in quickly deciding his course of action, and his skilful method of attacking against such great odds, removed a dangerous obstacle to the advance of the troops on the right, and inspired the remainder of our small party with the utmost confidence when advancing to the objective line.
— The London Gazette, No. 30733, 4 June 1918.