The event related potential (ERP) brain-computer interface (BCI) system extensively uses the scalp electroencephalogram (EEG) for communication and motor control. It is a non-invasive procedure and the signal record has ERPs buried in EEG due to its low strength and it is usually contaminated with artefacts. For BCI control applications, the ocular artefacts produced by eye movement and blink which are dominant over the other physiological artefacts are undesirable. The objective of the study is to effectively remove the ocular artefact from EEG using discrete wavelet transform (DWT) combined with recursive least mean square (RLS) adaptive noise cancellation technique using the optimal basis function with Stein's unbiased risk estimate (SURE) thresholding. The proposed methodology is tested on the datasets created from the experimental setup measuring the performance metrics - mean square error (MSE), artefact to signal ratio (ASR), correlation coefficient and coherence. The results show that db4 wavelet performs better in de-trending and ocular artefact suppression by providing better signal to noise ratio and high level of coherence from 5 Hz onwards while preserving the original EEG signal.