Ah, well here lies a problem with the interweb, because this London stone wiki page does mention it...
https://en.wikipedia.org/wiki/London_Stone_(riparian) which also has a picture of the Staines stone complete with grooves worn by tow-ropes!
Also, another interesting thing about St Aines (you knew there was more than one, right?) is this little bollard
There's another one buried in undergrowth by what is now Regus offices, and another by the towpath near Halfords.
They are excise markers. If you passed these markers going into London carrying coal or wine, you were liable to pay a duty which, I believe, helped pay for the bridges across the tideway!
(I have passed the Halfords one on the way back from Sainsbury's many times, but I think my wine was duty paid...)
Ah, now there you have me. I thought they owned it as part of the port, but it isn't a hill I am willing to die on.
Sorry for the thread drift, but when you live somewhere as dull as Staines, it's good to find some interesting bits that don't involve Sacha Baron Cohen...😁