Hydrogen presents an attractive option to decarbonise the present energy system. Hydrogen can extend the usage of the existing gas infrastructure with low-cost energy storability and flexibility. Excess electricity generated by renewables can be converted into hydrogen. In this paper, a novel multi-energy systems optimisation model was proposed to maximise investment and operating synergy in the electricity, heating, and transport sectors, considering the integration of a hydrogen system to minimise the overall costs. The model considers two hydrogen production processes: (i) gas-to-gas (G2G) with carbon capture and storage (CCS), and (ii) power-to-gas (P2G). The proposed model was applied in a future Great Britain (GB) system. Through a comparison with the system without hydrogen, the results showed that the G2G process could reduce £3.9 bn/year, and that the P2G process could bring £2.1 bn/year in cost-savings under a 30 Mt carbon target. The results also demonstrate the system implications of the two hydrogen production processes on the investment and operation of other energy sectors. The G2G process can reduce the total power generation capacity from 71 GW to 53 GW, and the P2G process can promote the integration of wind power from 83 GW to 130 GW under a 30 Mt carbon target. The results also demonstrate the changes in the heating strategies driven by the different hydrogen production processes.