I remember walking past there and over the Penny Bridge with my father when I was a child. I used to hate going over the bridge because I could see the water through the slats of the footway and it scared me. There was a large floating crane there called The Mammoth, if memory serves. Dad suggested I put my foot on the edge of it and try to push it! This was, presumably, in the days before dockside Health & Safety. I should add that he was a very careful father, but with a wicked sense of humour.
If you Google Mammoth floating crane Birkenhead there are quite a few things online; here's a link to a short vid from the 60s of the Titan, similar to the Mammoth. https://www.youtube.com/watch?v=v-GtdeDO0rM