I agree with Codeswitcher's comment. Judges live in a world of precise language that assigns technical meaning to ordinary words and obsolete usages. The judgement is not the order. The judgement is the implied answer to the question "What would you rule on this issue?". The statement "I would dismiss this appeal." answers that question. There then follows an order, which is the event that actually takes effect. Especially when there are multiple judges - the first to speak cannot say "I dismiss the appeal", he has to use a statement in the conditional future tense until the other judges have spoken.
I conducted a quick survey of older cases on Bailii to test this. The oldest from 1883: http://www.bailii.org/ew/cases/EWCA/Civ/1883/1.html does not have this exact form, but the subjunctive is all over the penultimate paragraph - "would" appears in a dozen places. "Carbolic smoke ball" is very different; no "would". "Wednesbury", the canonical discussion of "unreasonable", has "this appeal must be dismissed". Which again is a statement about the future rather than saying "I dismiss this appeal".
Endacott has the "would" formulation. I suspect it's much, much older than 1959 though.