Kulhavy’s regularised parameter identification concept protects the adaptive recursive estimation of a linear regression model from numerical difficulties associated with standard exponential weighting in cases where the processed data is not sufficiently exciting. Unfortunately, such robustness incurs a severe penalty in computational complexity, which militates against practical applications. This paper presents a new block regularised parameter estimator that is compatible with the requirements for implementation on a parallel architecture. Owing to the accumulated regularisation in blocks, the achieved throughput of the estimator is an order of magnitude higher in comparison with the general framework of Kulhavy and more comparable to recursive least squares on a systolic array. The processing cells operate at almost 100% efficiency, and are only connected to their nearest neighbours by one-directional connections. This new parameter estimator offers significant potential for identification, adaptive filtering and adaptive control applications, particularly in the real-time domain.