Precise timing over timestamped packet exchange communication is an enabling technology in the mission-critical industrial Internet of Things, particularly when satellite-based timing is unavailable. The main challenge is to ensure timing accuracy when the clock synchronisation system is subject to disturbances caused by the drifting frequency, time-varying delay, jitter, and timestamping uncertainty. In this work, a Robust Packet-Coupled Oscillators (R-PkCOs) protocol is proposed to reduce the effects of perturbations manifested in the drifting clock, timestamping uncertainty and delays. First, in the spanning tree clock topology, time synchronisation between an arbitrary pair of clocks is modelled as a state-space model, where clock states are coupled with each other by one-way timestamped packet exchange (referred to as packet coupling), and the impacts of both drifting frequency and delays are modelled as disturbances. A static output controller is adopted to adjust the drifting clock. The H∞ robust control design solution is proposed to guarantee that the ratio between the modulus of synchronisation precision and the magnitude of the disturbances is always less than a given value. Therefore, the proposed time synchronisation protocol is robust against the disturbances, which means that the impacts of drifting frequency and delays on the synchronisation accuracy are limited. The one-hour experimental results demonstrate that the proposed R-PkCOs protocol can realise time synchronisation with the precision of six microseconds in a 21-node IEEE 802.15.4 network. This work has widespread impacts in the process automation of automotive, mining, oil and gas industries.