The lack of clarity and uncertainty about hydrogen's role, demand, applications, and economics has been a barrier to the development of the hydrogen economy. In this paper, an optimisation model for the integrated planning and operation of hydrogen and electricity systems is presented to identify the role of hydrogen technologies and linepack in decarbonising energy systems, improving system flexibility, and enhancing energy system security and resilience against extreme weather events. The studies are conducted on Great Britain's (GB) 2050 net-zero electricity and gas transmission systems to analyse the hydrogen transport and capacity requirements within the existing infrastructure under different scenarios. This includes sensitivities on the level of flexibility, high gas prices, hydrogen production mixes, enabled reversibility of electrolysers, electricity generation cost, and hydrogen storage facilities. In all sensitivity scenarios, efficient hydrogen transport within the existing infrastructure is enabled by the optimal allocation of green and blue hydrogen sources, distributed storage facilities, and the intra-day flexibility provided by linepack. The findings highlight that increased renewable deployment transfers intermittency to the hydrogen network, requiring greater linepack flexibility compared to the current paradigm (up to 83%). Furthermore, the necessity of synergy between different gas and electricity systems components in providing flexibility, security, and resilience is quantified.