Multi-hazard risk assessment may provide comprehensive analysis of the impact of multiple hazards but still needs to resolve major challenges in three aspects: (1) proper consideration of hazard inter-dependency, (2) physically based modelling of hazard interactions, and (3) fully quantitative risk assessment to show the probability of loss. Compound flooding is a typical multi-hazard problem that involves the concurrence of multiple hazard drivers, e.g. heavy rainfall, extreme river flow, and storm surge. These hazard drivers may result from the same weather system and are thus statistically inter-dependent, physically overlayed and interacted in the same region. This paper aims to address the mentioned challenges and develop an integrated assessment framework to quantify compound flood risk. The framework is constructed based on the three typical components in disaster risk assessment, i.e. hazard, vulnerability and exposure analysis. In hazard analysis, joint probability and return period distributions of the three hazard drivers of compound flooding are estimated using Copula functions with hazard dependency analysis, which are then used to generate random multi-hazard events to drive a 2D high-performance hydrodynamic model to produce probabilistic inundation maps and frequency-inundation curves. Vulnerability and exposure analysis provides damage functions of the elements at risk, which are used to quantify multi-hazard risk with the frequency-inundation curves. The framework is applied in the Greater London and its downstream Thames estuary to demonstrate its capability to analyse hazard interactions and inter-dependencies to produce fully quantitative risk assessment results such as risk curves quantifying the probability of loss and risk maps illustrating the annual expected loss of residential buildings.