1920! That's shocked me mate, I don't know why I thought it was put there to commemorate something in the 1970's.
The many things around Sefton Park all placed there or adapted, prior to the first world war were all based around J.M.Barrie's Peter Pan.(published 1911)
The Fairy glen, The Jolly Roger in the lake, even the statue itself of Peter Pan, with all of the animals on etc., so 1920 for the boat would fit just fine.
Personally, I always remember it most from the late 1970s, when we used to go on school trips to the park (I'm from the north end), when the boat was mostly a little bit shabby.
I think it was eventually removed in the late 80s or early 90s after repeated vandal attacks, and possibly being set on fire.
Shame. It was a very iconic boat on the lake, which makes me quite nostalgic seeing it in that photo, when it's all brand new, with it's masts and rigging intact and everything.
She really must of been a beauty in her day.