Background The 2016 Childhood Obesity Plan included a target of 60 min(m) daily moderate-vigorous physical activity (dMVPA). In the UK Millennium Cohort Study (~18 000 children born 2000–2002) we examined how the prevalence and social distribution of childhood overweight/obesity might change if physical activity (PA) interventions aimed at this target were rolled-out under different scenarios of eligibility, uptake and effectiveness.

Methods dMVPA at 7 years(y) was captured with accelerometers, over one week, adjusted for total wear-time. At 11y, children were classified as healthy, overweight (including obese), using measured heights and weights and International Obesity Task Force cut-offs. Socio-economic circumstances (SECs) were represented by maternal education (GCSEs/None; A-Levels+).

Predicted probabilities of overweight were estimated by fitting marginal structural models, adjusting for dMVPA, and accounting for baseline and intermediate confounding with inverse-probability-treatment-weights. Inequalities were assessed with risk ratios (RRs) and risk differences (RDs). Intervention scenarios were simulated by re-estimating predicted probabilities after modifying the dMVPA variable by a given amount (reflecting effectiveness), for eligible children only (for targeted interventions), and with random sampling (where uptake <100%).

Analyses included 6344 children in the MCS PA study. Survey weights and multiple imputation addressed sampling design, attrition and item missingness. Sensitivity analyses using complete cases and alternative adiposity (fat mass) and SECs (income) measures produced similar conclusions.

Results 28.4% children were overweight and those from lower SECs were at greater risk (RR: 1.36 [95% CI: 1.25–1.49]; RD: 9.6%[9.2–9.9]). 49% achieved 60 m dMVPA, although mean dMVPA was greater in low SECs groups (64.5 m vs. 61.8 m).

Simulations showed that, with an additional 30 m dMVPA for all children, 96% would achieve 60 m dMVPA. Prevalence of overweight would decline significantly (to 22.4%), relative inequality would increase (RR 1.40 [1.27–1.55]), whereas absolute inequality would fall slightly (RD 8.3%[8.0–8.6]).

More realistic simulations, using effect sizes from meta-analyses and assuming 77% uptake, were less promising. A universal 4.6 m increase in dMVPA would lead to negligible reductions in overweight (27.7%), with no change in inequality (RR 1.37 [1.26–1.49]; RD 9.5%[9.2–9.8]). Intensive, targeted interventions achieving an additional 9.6 m dMVPA in deprived neighbourhoods would not alter population-level prevalence of overweight (28.1%) or inequality (RR 1.35 [1.24–1.47]; RD 9.1%[8.7–9.4]).

Conclusion A simulation of the government’s ambitious PA target (in nationally-representative, objective data) achieved only a moderate reduction in population prevalence of childhood overweight and a slight narrowing of absolute (but not relative) inequalities. More realistic scenarios (modelling effects of trialled interventions) did not reduce prevalence of overweight and, even when targeted at deprived areas, inequalities remained.