This story is literally older than the internet, and widely know to not really be true. I'm sure almost anyone on this website has read of version of this hosted on some basic HTML site at least a decade ago.
England actually had at least one more competing gauge: Brunel gauge. Brunel thought it was silly to keep using the same arbitrary gauge and that a broader gauge would be more comfortable. Eventually it was decided to use the Stephenson gauge instead, though, and this became "standard" gauge.
It's an interesting example of a compromise where having just one standard is preferable to trying to find the perfect standard.
[0] https://www.snopes.com/fact-check/railroad-gauge-chariots/