Having sequenced thousands of tumour genomes, they found a 20-a-day smoker would rack up an average of 150 mutations in every lung cell each year.
The changes are permanent, and persist even if someone gives up smoking.
Researchers say analysing tumour DNA may help explain the underlying causes of other cancers.
Pamela Pugh, 69, was diagnosed with lung cancer in 2013. She started smoking aged 17 and quit in her early 50s.
But she said: "Even though I gave up many years ago, the effects of smoking caught up with me.