Deep decarbonisation of the electricity sector is central to achieving the United Kingdom's (UK) climate policy targets for 2050 and meeting its international commitments under the Paris Agreement. While the overall strategy for decarbonising the energy system has been well established in previous studies, there remain deep uncertainties around the total investment cost requirements for the power system. The future of the power system is of critical importance because low carbon electricity may create significant opportunities for emissions reduction in buildings and transport. A key policy application of quantitative analysis using models is to explore how much investment needs to be mobilised for the energy transition. However, past estimates of energy transition costs for the UK power sector have focused only on 2030 rather than 2050 and consider a relatively narrow range of uncertainties. This paper addresses this important research gap. The UK government's main whole system energy economy model is linked to a power system model that employs an advanced approach to uncertainty analysis, combining Monte Carlo simulation with Modelling-to-Generate Alternatives (MGA), producing 800 different scenario pathways. These pathways simultaneously consider uncertainties in policy, technology and costs. The results show that with No Climate Policy, installed generation capacities in 2050 are found in the range 60–75 GW, while under an 80% Reduction in GHG Emissions, between 100 GW and 130 GW of plant are required. Meeting climate targets for 2050 is also found to increase the investment requirements for new electricity generation. The interquartile range for cumulative investments in new generation under the No Climate Policy scenario ranges from £60bn to £75bn, while under an 80% Reduction in GHG Emissions, investment requirements approximately double to £110bn - £140bn. The exercise demonstrates the importance of uncertainty analysis to policy evaluation, yielding insights for future research practice both in the UK and internationally.