Objectives Many smokers use e-cigarettes and licensed nicotine replacement therapy (NRT), often in an attempt to reduce their cigarette consumption. We estimated how far changes in prevalence of e-cigarette and NRT use while smoking were accompanied by changes in cigarette consumption at the population level. Design Repeated representative cross-sectional population surveys of adults aged 16+ years in England. Methods We used Autoregressive Integrated Moving Average with Exogeneous Input (ARIMP modelling of monthly data between 2006 and 2016 from the Smoking Toolkit Study. Prevalence of e-cigarette use and NRT use in current smokers, and specifically for smoking reduction and temporary abstinence, were input variables. Mean daily cigarette consumption was the dependent variable. Analyses involved adjustment for mass media expenditure and tobacco-control policies. Results No statistically significant associations were found between changes in use of e-cigarettes (beta -0.012, 95% CI -0.026 to 0.002) or NRT ((3 0.015, 95% CI -0.026 to 0.055) while smoking and daily cigarette consumption. Neither did we find clear evidence for an association between e-cigarette use (beta -0.010, 95% CI -0.025 to 0.005 and beta 0.011, 95%-0.027 to 0.004) or NRT use (beta 0.006, 95%-0.030 to 0.043 and beta 0.022, 95%-0.020 to 0.063) specifically for smoking reduction and temporary abstinence, respectively, and changes in daily cigarette consumption. Conclusion If use of e-cigarettes and licensed NRT while smoking acted to reduce cigarette consumption in England between 2006 and 2016, the effect was likely very small at a population level.