A mathematical model for the COVID-19 pandemic spread, which integratesage-structured Susceptible-Exposed-Infected-Recovered-Deceased dynamics with realmobile phone data accounting for the population mobility, is presented. The dynamicalmodel adjustment is performed via Approximate Bayesian Computation. Optimallockdown and exit strategies are determined based on nonlinear model predictivecontrol, constrained to public-health and socio-economic factors. Through an extensivecomputational validation of the methodology, it is shown that it is possible to computerobust exit strategies with realistic reduced mobility values to inform public policymaking, and we exemplify the applicability of the methodology using datasets fromEngland and France.