Burke was part of Bonington's 1975 Everest expedition, again to climb the south-west face. Burke's role was primarily as a climber, but he also provided high altitude film coverage for the BBC film crew accompanying the expedition. Following Dougal Haston and Doug Scott's first ascent of the face and successful climb to the summit, Burke was part of a second summit push, from which he did not return. He was last seen alive heading upwards, a few hundred metres from the summit, but it is not known for sure that he reached the highest point. The weather began to deteriorate rapidly just after he was last seen, and within hours storms had set in which lasted for two days, precluding any rescue attempt by his companions who were themselves marooned in the top camp until the storms abated. His body was never recovered.