The tunnelling of quasiparticles across Josephson junctions in superconducting quantum circuits is an intrinsic decoherence mechanism for qubit degrees of freedom. Understanding the limits imposed by quasiparticle tunnelling on qubit relaxation and dephasing is of theoretical and experimental interest, particularly as improved understanding of extrinsic mechanisms has allowed crossing the 100 microsecond mark in transmon-type charge qubits. Here, by integrating recent developments in high-fidelity qubit readout and feedback control in circuit quantum electrodynamics, we transform a state-of-the-art transmon into its own real-time charge-parity detector. We directly measure the tunnelling of quasiparticles across the single junction and isolate the contribution of this tunnelling to qubit relaxation and dephasing, without reliance on theory. The millisecond timescales measured demonstrate that quasiparticle tunnelling does not presently bottleneck transmon qubit coherence, leaving room for yet another order of magnitude increase.