The decarbonisation of the power sector is key to achieving the Paris Agreement goal of limiting global mean surface temperature rise to well below 2 degrees C. This will require rapid, national level transitions to low carbon electricity generation, such as variable renewables (VRE), nuclear and fossil fuels with carbon capture and storage, across the world. At the same time it is essential that future power systems are sustainable in the wider sense and thus respect social, environmental and technical limitations. Here we develop an energy-land-water nexus modelling framework and use it to perform a scenario analysis with the aim of understanding the planning and operational implications of these constraints on Great Britain's (GB) power system in 2050. We consider plausible scenarios for limits on installed nuclear capacity, siting restrictions that shape VRE deployment and water use for thermal power station cooling. We find that these factors combined can lead to up to a 25% increase in the system's levelised cost of electricity (LCOE). VRE siting restrictions can result in an up to 13% increase in system LCOE as the deployment of onshore wind is limited while nuclear capacity restrictions can drive an up to 17% greater LCOE. We also show that such real-world limitations can cause substantial changes in system design both in terms of the spatial pattern of where generators are located and the capacity mix of the system. Thus we demonstrate the large impact simultaneously considering a set of nexus factors can have on future GB power systems. Finally, given our plausible assumptions about key energy-land-water restrictions and emission limits effecting the GB power system in 2050, the cost optimal penetration of VREs is found to be at least 50%.