What is the principle of presumption of bias in the context of judicial review?

Vaughan Williams L.J. in Rex v. Sunderland Justices, [1901] 2 K.B. 357 at 371, enunciated the principle with this statement: "If he has personally a pecuniary interest or an interest capable of being measured pecuniarily, the law raises a conclusive presumption of bias. For reasons of policy, which hardly require explanation, it is not thought convenient, where there is such an interest, to go into the question whether he in fact acted partially or impartially. A bias is presumed from the mere fact of the existence of the interest."