And the number of smokers who successfully managed to stop smoking increased by just under 1% for every 1% rise in the number of smokers using e-cigarettes.
Use of prescribed nicotine-replacement therapy also fell as e-cigarette use rose.
The team, led by Prof Robert West at UCL, said: “The increased prevalence of e-cigarettes in England does not appear to have been associated with a detectable change in attempts to stop smoking.
“However, the increase in e-cigarette use has been associated with an increase in success of quit attempts.”
Writing in the BMJ, John Britton, director of the UK Centre for Tobacco and Alcohol Studies at the University of Nottingham, said the results suggested e-cigarette use could contribute to falling smoking rates.
Smoking rates fell by 1% from 2014 to 2015.
Dr Britton said: “This significant year-on-year fall indicates that something in UK tobacco control policy is working, and successful quitting through substitution with e-cigarettes is one likely major contributor.”
Prof Linda Bauld, of Cancer Research UK, said: “The British public have voted with their feet and are choosing to use e-cigarettes. This is a positive choice, and we should promote it.”
Public Health England says e-cigarettes are 95% less harmful to your health than normal cigarettes, and when supported by a smoking cessation service, help most smokers to quit tobacco altogether.