The integration of cardiac magnetic resonance (CMR) imaging and electrocardiogram (ECG) data through advanced computational methods could enable the development of the cardiac ‘digital twin’, a comprehensive virtual tool that mechanistically reveals a patient’s heart condition from clinical data and simulates treatment outcomes. The adoption of cardiac digital twins requires the non-invasive efficient personalisation of the electrophysiological properties in cardiac models. This study develops and evaluates new computational techniques to estimate key ventricular activation properties for individual subjects by exploiting the synergy between CMR, ECG, and modelling and simulation. We present an efficient sequential Monte Carlo approximate Bayesian computation-based inference method, integrated with Eikonal simulations and torso-biventricular models constructed based on clinical CMR imaging to recover conduction speeds and earliest activation sites from 12-lead ECGs. We demonstrate successful results of our inference method on a cohort of twenty virtual subjects with cardiac ventricular myocardial-mass volumes ranging from 74 cm3 to 171 cm3.