I also though the Woodward was a sidelock, but wasn't sure enough to post. There was a Joseph Lang push forward underlever that was certainly a trigger plate action. I had one and it was a nice gun with a top strap safety that was a 1/8 turn type design; sounds awkward, but was in fact easy to use and very easy to see if applied or not.
Safety catches and 'loaded indicators' were apparently a big concern on early hammerless guns as users struggled with the idea that it was always at 'full cock', having been used to visible hammers.