This paper develops a novel approach for distribution system monitoring and state estimation, where time synchronisation of smart-meter measurements is carried out via the Precision Time Protocol (PTP). The approach is based on the concept of a Modified Smart Meter (MSM), a distribution system monitoring instrument that enables accurate time synchronisation of smart meter data. The design, application, communication technique and protocols of the MSM are described in detail. The proposed MSM device features PTP-based time synchronisation of smart meter measurements, and the concept of unbundling is applied to collect measurements utilising the existing smart meter sensors. This is expected to reduce the overall implementation cost of an MSM-based distribution network monitoring system compared to a system based on Phasor Measurement Units (PMUs). The problem of requiring open sky access for GPS links can potentially be solved by means of PTP synchronisation. Three-phase state estimation simulations using the IEEE-13 and 123 bus unbalanced test networks are employed to demonstrate the applicability of the MSM, and its performance is compared to standard PMU devices. The results indicate that the MSM may represent a workable monitoring solution for MV and LV distribution networks, with an acceptable trade-off between cost and performance.