That isn’t ‘a’ trade mark journal: it’s the Trade Marks Journal, the official gazette of the Patent Office in London, in which trademarks applied for and granted were and are listed (now online at https://www.ipo.gov.uk/t-tmj.htm). So presumably that is the actual date on which shoes called plimsolls began to exist.
I have always been given to understand that the shoes were given that name as the level white band around joining the upper to the sole reminded people of the Plimsoll line on a ship’s hull; the Wikipedia entry on Plimsoll shoe cites one Nicholette Jones’s book The Plimsoll Sensation, which gives that as one possible reason but also suggests that an alternative reason might be that this band had a similar function to the the Plimsoll line on a ship’s hull: viz. that, if water got above the line, the wearer would get wet.
Either way, there seems to be no doubt that the shoe was named after the Plimsoll Line. Samuel Plimsoll fought a long and very public campaign for legislation to impose a safe load line on merchant vessels; popular periodicals such as Punch carried articles and cartoons on the subject. So the Plimsoll Line was far more familiar to the general public then than it is now.