The deployment of smart hybrid heat pumps can introduce considerable benefits to electricity systems via smart switching between electricity and gas while minimizing the total heating cost for each individual customer. In particular, the fully-optimized control technology can provide flexible heat that redistributes the heat demand across time for improving the utilization of low-carbon generation and enhancing the overall energy efficiency of the heating system. To this end, accurate quantification of preheating is of great importance to characterize the flexible heat. This paper proposes a novel data-driven preheating quantification method to estimate the capability of heat pump demand shifting and isolate the effect of interventions. Varieties of fine-grained data from a real-world trial are exploited to estimate the baseline heat demand using Bayesian deep learning while jointly considering epistemic and aleatoric uncertainties. A comprehensive range of case studies are carried out to demonstrate the superior performance of the proposed quantification method and then, the estimated demand shift is used as an input into the whole-system model to investigate the system implications and quantify the range of benefits of rolling-out the smart hybrid heat pumps developed by PassivSystems to the future GB electricity systems.