The paper examines the combined effects of several interacting thermo-acoustic and hydrodynamic instability mechanisms that are known to influence self-excited combustion instabilities often encountered in the late design stages of modern lowemission gas turbine combustors. A compressible large eddy simulation approach is presented, comprising the flame burning regime independent, modelled probability density function evolution equation/stochastic fields solution method. The approach is subsequently applied to the PRECCINSTA (PREdiction and Control of Combustion INSTAbilities) model combustor and successfully captures a fully self-excited limit-cycle oscillation without external forcing. The predicted frequency and amplitude of the dominant thermo-acoustic mode and its first harmonic are found to be in excellent agreement with available experimental data. Analysis of the phaseresolved and phase-averaged fields leads to a detailed description of the superimposed mass flow rate and equivalence ratio fluctuations underlying the governing feedback loop. The prevailing thermo-acoustic cycle features regular flame lift-off and flashback events in combination with a flame angle oscillation, as well as multiple hydrodynamic phenomena, i.e. toroidal vortex shedding and a precessing vortex core. The periodic excitation and suppression of these hydrodynamic phenomena is confirmed via spectral proper orthogonal decomposition and shown to be controlled by an oscillation of the instantaneous swirl number. Their local impact on the heat release rate, which is predominantly modulated by flame-vortex roll-up and enhanced mixing of fuel and oxidiser, is further described and investigated. Finally, the temporal relationship between the flame 'surface area', flame-averaged mixture fraction and global heat release rate are found to be directly correlated.