HHJ McMullen QC (sitting alone in the EAT) considered this question in Mitchell v St Josephs School. He noted the transition from the "industrial jury" to judges sitting alone in unfair dismissal cases. But, he said the law is the same. In applying it, he suggested the role of a judge sitting alone is akin to a judicial review of the employer's procedure and decision.
On the facts of the case, the school bursar had failed to disclose the parlous state of the school's finances to the Board of Governors.
The EAT agreed with the employment tribunal that his dismissal was within the band of reasonable responses and therefore fair. Nor could the position be saved by the fact that the bursar had disclosed the state of affairs to two members of the Board. Applying the company law on attribution in Meridian Global Funds Management Asia Limited v Securities Commission  2 AC 500 and Orr v Milton Keynes Council, this did not mean the Board itself had knowledge of the finances.
In the appeal it was suggested that the Employment Judge had nonetheless adopted a subjective approach as to whether the dismissal was fair. The Judge's language, in using the first person singular, had laid himself open to this suggestion.
In the end it was considered, however, that the Judge directed himself correctly on the authorities and applied the law to the facts accordingly.