The 5‐year relative survival of adults diagnosed with acute myeloid leukaemia (AML) was less than 10% during the 1970s and 1980s in England. This population‐based study estimated the 5‐year relative survival and ‘cure’ for 48 380 adult patients diagnosed with AML in England during 1971–2006. Relative survival and cure mixture models were used to produce estimates of 5‐year relative survival and the percentage ‘cured’. ‘Cure’ was defined as the proportion of a group of survivors for whom there is no excess mortality compared with the general population. The 5‐year relative survival and the percentage ‘cured’ increased for patients aged under 70 years at diagnosis during 1971–2006, but advancing age was associated with poorer outcome. During the study period a dramatic increase in 5‐year relative survival occurred in those aged 15–24 years, from 7% to 53%. The percentage ‘cured’ was less than 10% for all ages in 1975, but increased to 45% for those aged 15–24 years in 2000. Cure could not be estimated for patients over 70 years, because survival was consistently low (<5%). The long‐term outcome of patients with AML has improved substantially, particularly in younger patients. The potential exists for further increasing levels of ‘cure’.