Sound source localisation is used in many consumer devices, to isolate audio from individual speakers and reject noise. Localization is frequently accomplished by ``beamforming'', which combines phase-shifted audio streams to increase power from chosen source directions, under a known microphone array geometry. Dense band-pass filters are often needed to obtain narrowband signal components from wideband audio. These approaches achieve high accuracy, but narrowband beamforming is computationally demanding, and not ideal for low-power IoT devices. We demonstrate a novel method for sound source localisation on arbitrary microphone arrays, designed for efficient implementation in ultra-low-power spiking neural networks (SNNs). We use a Hilbert transform to avoid dense band-pass filters, and introduce a new event-based encoding method that captures the phase of the complex analytic signal. Our approach achieves state-of-the-art accuracy for SNN methods, comparable with traditional non-SNN super-resolution beamforming. We deploy our method to low-power SNN inference hardware, with much lower power consumption than super-resolution methods. We demonstrate that signal processing approaches co-designed with spiking neural network implementations can achieve much improved power efficiency. Our new Hilbert-transform-based method for beamforming can also improve the efficiency of traditional DSP-based signal processing.