The answer appears surprisingly simple: step forward the little-known (some might even say shy) sub-section 54(5) of the Senior Courts Act 1981, where it is stated that:
“…the case shall, on the application of any party to the appeal, be re-argued before and determined by an uneven number of judges not less than three, before any appeal to the Supreme Court.”
Especially bearing in mind that Court of Appeal cases are frequently heard by two judges instead of three, what seems even more surprising is that one does not (or at least I do not) often hear of Court of Appeal cases where a 1-1 draw has occurred. If you have worked on such a 1-1 draw case, please do let me know (in the comment box below) how sub-section 54(5) worked out for you. I suspect it results in parties having to incur quite a lot of additional irrecoverable costs. A 1-1 draw appeal that I have heard of (Farley v Skinner) started off with an initial two-judge Court of Appeal hearing, but ended up being heard by a total of five Court of Appeal judges during two Court of Appeal hearings (and was ultimately heard and determined by five more judges in the House of Lords).
Shortly after a Court of Appeal’s initial two-judge hearing results in deadlock, I imagine an interesting discussion probably takes place between the judges concerning the reasons they do not concur (see the brief mention, in the judgment of Stuart-Smith LJ, of a discussion that took place between the judges involved in the Court of Appeal case Nipa Begum v Tower Hamlets London Borough Council, after its initial two-judge hearing resulted in a possible disagreement). In the interests of open justice, perhaps such discussions should take place in a courtroom open to the public. In fact, maybe all post-hearing (but pre-judgment) case-related discussions between appeal court judges should take place in open court, including when they occur in Supreme Court proceedings. Now that would be fascinating!