The reliability and availability of network connectivity, which significantly varies with mobility, is crucial in Connected, Cooperative and Automated Mobility (CCAM). Handover and roaming are the most challenging situations in terms of connectivity of cellular networks, which require switching across cells of the same cellular network or between Public Land Mobile Networks (PLMNs). This paper proposes a set of solutions for vehicular applications to mitigate the impact of mobility in service continuity, including a dual modem solution that reduces the interruption time when switching PLMNs, an adaptive bitrate mechanism for media streaming that increases reliability, a WebRTC server acting as a gateway in media streaming sessions between vehicles, and a MEC discovery and handover method. The proposed solutions have been evaluated executing an Extended Sensors application in several commercial and experimental 5G Non-Standalone (NSA) and Stand Alone (SA) setups with different Multi-access Edge Computing (MEC), edge-cloud and cloud infrastructures to host services. It can be concluded from the results obtained that 5G networks have not yet achieved the required performance for CCAM, and that practitioners need to implement solutions and workarounds, such as the ones proposed in this work, to mitigate the issues. As lessons learnt from the deployment and experimentation, this paper also overviews a detailed set of problems and the proposed solutions that CCAM industry and cellular network stakeholders need to consider.INDEX TERMS 5G, MEC, CCAM, inter-PLMN handover, vehicular communications, testing.