In the context of intra-body communication, gal-vanic coupling has gained significant attention. This communication technique leverages conductivity of biological tissues to use them as a medium for modulated electrical signals. This paper introduces a novel fully-digital demodulation technique for use in galvanic coupling transmission with BPSK-modulated signals at low frequencies (below MHz). The technique relies on an original digital processing algorithm applied on samples collected by an analogue-to-digital converter. The algorithm employs a voting principle among several demodulated data candidates and implement an error detection scheme to offer high robustness and reliability. Moreover, it has been specifically designed to minimise the computational operations and resources required to enable a compact and energy-efficient implementation. Simulations and experiments demonstrate good performance, with a perfect transmission success rate of 100% for signals with a Signal-to-Noise Ratio (SNR) of -3 dB or higher, and a success rate that remains higher than 97% for signals with an SNR down to -7dB.