Had the motion been passed, it would probably have needed the approval of parliament to bring the change about.
The previous version of the story mentioned it in this way:
The practice is so old that it is not clear whether it is simply custom or if Parliament would have to change it.
Oaths sworn on the Bible are old enough for the Magistrates’ Association to be unsure whether they are mere custom and practice or whether they were laid down by law.
So, whatever the decision in Cardiff, it might need the approval of Parliament to bring the change about.
I found this quite unusual: changes to the law were being proposed, but the people proposing the changes didn’t actually know how they would go about changing it! Even in the final version of the story, the most informative that the writer could be about how the law would have been changed if the vote had approved it, was saying it would “probably” be done via Parliament!
I’m just glad I wasn’t the law librarian being asked to research when the Bible and holy book oaths had first been used in the courts, and under which powers they had been created!