Cardiac modelling and simulation have emerged as indispensable tools in unravelling the intricacies of disease mechanisms within the realm of cardiology. Although substantial progress has been achieved in comprehending cardiac functions, obtaining a holistic understanding of cardiology necessitates an exploration of the intricate interactions among diverse biophysical processes within the cardiovascular system, including haemodynamics. Despite advancements in modelling, the constraints of resources often confine these models to the complexities of the heart, leading to assumptions about external factors through techniques such as reduced-order modelling. One potential remedy involves the integration of independently developed models. However, this presents significant technical challenges, compounded by the practical obstacle of limited accessibility to multiple models simultaneously. In this context, we present an innovative endeavour to couple the 3D electro-mechanical model of the heart in Alya [1] with the 3D fluid mechanics model of the blood vessels in HemeLB [2]. These models have been created by separate research groups, emphasizing different dynamical scales, utilizing distinct discretisation schemes (finite-element method vs. lattice Boltzmann method), and implemented in distinct programming languages (Fortran vs. C++). Leveraging the excellent scaling performance of these models on supercomputers, our objective is to construct a unified and highly efficient multi-physics model. Through a series of test simulations spanning multiple cardiac cycles and geometries, we demonstrate the viability of a staggered coupling scheme for this particular scenario. We also delve into a discussion of the coupled model's robustness, numerical stability and computational efficiency. Moreover, by implementing the proposed model in a practical context involving a realistic heart-vessels configuration, we provide initial insights into its potential application using high-performance computers in large-scale scenarios. [1] M. Vázquez et al., Alya: Multiphysics engineering simulation toward exascale. J. Comput. Sci., Vol. 14, pp. 15-27, 2016. [2] M.D. Mazzeo and P.V. Coveney, HemeLB: A high performance parallel lattice-Boltzmann code for large scale fluid flow in complex geometries. Comput. Phys. Commun., Vol. 178, pp. 894-914, 2008.