As a result, he says Cpl Sarah Bryant - the first female soldier to die in Afghanistan - and three male colleagues, Cpl Sean Reeve, L/Cpl Richard Larkin and Paul Stout were killed needlessly, The Telegraph reported.
All four died when their lightly armoured Snatch Land Rover split apart after hitting a landmine in Helmand province in June.
In his resignation letter, Major Morley, the commander of D Squadron, 23 SAS, said "chronic under investment" in equipment by the Ministry of Defence was to blame for their deaths.
The Old Etonian officer, a cousin to the late Diana, Princess of Wales, is understood to have described the MoD's failure to buy better equipment as "cavalier at best, criminal at worst."
The resignation of Major Morley, the grandson of the newspaper tycoon Lord Beaverbrook, follows those of Colonel Stuart Tootal, Brigadier Ed Butler and a commanding officer of 22 SAS.
"We highlighted this issue saying people are going to die and now they have died," said a soldier who served with Major Morley.
"Our commanding officer and RSM (Regimental Sergeant Major) tried everything in their power to stop us using Snatch. The point of failure here lies squarely with the MoD. The boys nicknamed Snatch the mobile coffin," the soldier added.
The resignation of Major Morley will re-ignite the debate on the standard of equipment for troops, with many front line soldiers believing that their lives are being put at risk.
In recent weeks the MoD has been criticised by coroners who said the right equipment could have saved lives.
The frailties of Snatch Land Rovers have been responsible for 34 British fatalities - or one in eight of the total killed in Iraq and Afghanistan. They are only now being replaced.