Just over a third - 36% - of breast cancer patients will ultimately die from their disease, down from 61% in 1992.
Some 36% of prostate cancer patients will also die, according to projections for 2020, down from 72% in 1992.
Almost two in five (39%) people with bowel cancer will die from their disease, down from 67% in 1992.
The data, from Macmillan Cancer Support, shows lung cancer lagging behind, with 76% of patients expected to die from their disease, against 91% in 1992.
Survival from lung cancer has been historically low, with experts suggesting a range of reasons, including people going to their GP too late with symptoms and unequal access to surgery depending on where people live.
Previous Macmillan research estimated that by 2020 almost half (47%) of people would get cancer in their lifetime and 38% would survive the disease.
Professor Jane Maher, chief medical officer of Macmillan Cancer Support, said: "People diagnosed with three of the four most common cancers are more likely to survive but GPs need more support to help them diagnose lung cancer earlier."
Ciaran Devane, the charity's chief executive, said three key things needed to be done to help reduce the number of lung cancer victims.
He said: "Firstly, we support the call for plain packaging of cigarettes to stop people taking up smoking.
"Secondly, we must catch the illness earlier through better awareness and we have to make sure access to surgery is more uniform across the country to reduce inequalities in cancer survival."