Objective: Spike sorting is a fundamental step in analysing extracellular recordings, enabling the isolation of single-neuron activity. However, it remains a challenging problem because extracellular traces mix overlapping spikes from neighbouring cells and are marred by recording instabilities such as electrode drift. Numerous algorithms have been proposed, yet many struggle to balance accuracy and computational efficiency, limiting their practicality for todays large-scale datasets. Approach: In response, we introduce SpikeSift, a spike-sorting algorithm expressly designed to mitigate drift while running on standard CPUs. SpikeSift (i) partitions long recordings into shorter, relatively stationary segments, (ii) carries out spike detection and clustering simultaneously through an iterative detect-and-subtract scheme within each segment, and (iii) preserves neuronal identity across segments via a fast template alignment stage that dispenses with continuous trajectory estimation. Main results: Extensive validation on paired intracellularly validated datasets and on biophysically realistic MEArec simulations covering elevated noise, diverse drift profiles, ultra short recordings and bursting activity, demonstrates that SpikeSift matches or exceeds the accuracy of state of the art methods while completing sorting an order of magnitude faster on a single desktop core. Significance: The combination of high fidelity, drift resilience, and modest computational demand renders SpikeSift broadly accessible while preserving data quality for downstream neurophysiological analysis