Do London Taxi Drivers Need A Bale Of Hay In Their Boot To Satisfy Arcane English Laws?

No, that was repealed.
However, there are a still a number of bizarre offences under the 19th Century Metropolitan Police Acts (there were 8 acts of such a name), which include carrying a ladder in the metropolitan area after the hours of darkness.
Such offences have NOT been repealed, but no longer constitute arrestable offences under the Police and Criminal Evidence Act (PACE).