Clearly we have a difference of opinion
We do. You are also disagreeing with the judge in the High Court.
I can only find this on the Mirror site, which suggests the opposite
The report in the Mirror covers is about the debate in the Court if Appeal, not the High Court judgement. As someone who is used to the way the Court of Appeal works this report is a little odd in that it refers to "the judge" when there are in fact three judges. However, these comments came during the submission on behalf of the Labour party so would have been one of the judges testing the strength of the case rather than offering a legal opinion. In the end the Court of Appeal did not even bother to mention misrepresentation in its judgement beyond reporting the views of the High Court and suggesting that the misrepresentation argument misled the judge, resulting in him giving too much emphasis to matters outside the rulebook and hence making the wrong decision.
Caroldecker has highlighted the relevant clause in the initial judgement. In relation to the arguments about implied terms and misrepresentation the judge said, "given the difficulty in implying terms into a contract such as this, and the clear indication on the website that membership of the Party was the subject of the Rule Book, had his main ground failed, it is unlikely that these alternatives would have found favour".
So the members' lawyers possibly brought the wrong case
Their lawyers, correctly, concentrated on the case most likely to win - breach of contract. They also put forward a number of other arguments, including misrepresentation, as alternatives should the main argument fail. As the main argument succeeded in the High Court the judge did not need to rule on the alternative arguments but, as per the comments above, he stated that they were unlikely to succeed.