The basic issue is summarized conveniently at para 140 of his judgment:
"the claim is for infringement of copyright in a literary work HBHG ["The Holy Blood and The Holy Grail"] by the writing of another literary work DVC ["The Da Vinci Code"]. The claim is about applying existing established principles of UK copyright law to the facts as they have emerged. The claim is of non-textual infringement in literary work. It is conceded that such a claim is unusual and because of its nature presents a greater difficulty of analysis than a textual infringement claim."
Non-literal copying cases may be rare in literature but not in other areas of copyright. They have been particularly common in software over the last 20 years ever since the Third Circuit's landmark decision in Whelan v Jaslow 797 F.2d 1222. Probably the classic case in English law (at least for balletomanes) is Massine v De Basil (1938) 173 Macg Cop Case.
While the judgment itself came as no surprise to most people, the the judge approach was laboured, to say the least. He allowed himself to become ensnared in the so-called ideas expression dichotomy. As Sir Hugh Laddie, Michael Prescott and Mary Vitoria once rather controversially put in (para 2.73 of the 2nd edition of "The Modern Law Of Copyright"), the simple proposition that there is no copyright in an idea as such "has frequently been stated in a more extreme form that there is no copyright in ideas and information but only in the form in which they are expressed." The authors added that like all pithy catchphrases, this is liable to lead to confusion that copyright law protects form - language for instance - but never substantive content. Alas, Sir Peter became ensnared in the confusion though in that trap he kept very good company (see Judge Learned Hand's judgment in Nichols v. Universal Pictures Corporation et al.(1930) 45 F.2d 119).
Copyright is essentially about conduct. A copyright is infringed by copying not by similarity. Similarity may evidence copying but making a work similar to the copyright work otherwise than by copying is perfectly permissible. If there was any nexus between the copyright work and the putative copy there is an infringement and it matters not whether the thing that is taken is a line of text, a plot or a character. Copying is established by showing objective similarity between the copyright work and putative copy and an opportunity to copy (see Francis, Day & Hunter v Bron  Ch 587). If the defendant can show a reason for the objective similarity such as functional exigency (e.g. there is only one way to express the thought) or derivation from a common source he can exonerate himself but, otherwise, he is presumed on the balance of probabilities to have infringed.
I have not yet had an opportunity to read either Holy Blood and Holy Grail or the Da Vinci Code (though summer holidays are approaching) but from what I can fathom from the evidence mentioned by the judge, there was simply not enough to shift the tactical burden of proof. The tragedy is that the judge didn't actually say so. If there is ever an appeal from that judgment, that will be the reason why.