Understanding the behaviour of high-temperature plasmas is one of the main pillars in the development of fusion energy. It involves the development, validation, and use of several numerical models to describe complex physical processes and their interactions. Integrated modelling brings different models together, coupling them via suitable interfaces. Often, there is a need to include specific physics phenomena, such as magnetohydrodynamics, plasma turbulence or transport. They are computationally demanding and require modern supercomputers for their analysis. In such cases, the complexity of running integrated modelling workflows, including the use of supercomputers should be managed transparently, hidden to the final user. In this paper, we present and implement a scheme to tackle the execution of large fusion workflows on modern supercomputers using container technologies and a tool for their remote submission. We successfully packed in a container image a very complex environment: international thermonuclear experimental reactor (ITER) integrated modelling & analysis suite (IMAS). Moreover, we run high-performance computing codes up to 3072 cores with performance loss of 3%. The ITER H&CD worklfow was executed on Marconi and for the first time ran in a cluster without an installation of the IMAS framework. The presented capabilities have demonstrated the feasibility of our approach on Marconi-Fusion, the European High-Performance Computer for fusion applications and have tested a relevant application within the integrated modelling community.