I'm a bit bemused at that "lost to time", as immediately before that it says:

The law requires a bale of straw to be hung from a bridge as a warning to mariners whenever the height between the river and the bridge’s arches is reduced, as it is at Charing Cross at the moment.

That seems clear enough! OK, the reason why it specifically has to be a bale of straw isn't obvious, but apart from that it seems very reasonable, just outdated.

Edit to add: straw does make sense as a makeshift crash barrier -- you'll notice if you hit it, but hopefully won't actually damage your ship. It seems like you would always just plough through and hit the actual bridge, though.

Bales of straw are a cheap, large, soft object you could always find nearby in the pre-motor car days. I can't think of a better object to require.

Why does everyone think it’s something to run into?

At night it’s a light. It’s obviously a notification system. You visibly see the bale of straw before you get to the bridge and you know to slow down and stop and investigate what the clearance issue is.

Yeah it's amazing (in a bad sense) how those bridge too low warnings are ignored most of the time

Well of course when you get stuck then it's too late.