Bus driver sacked OMG

[King Billy]

I agree that if you chase someone with a weapon, with no intention of arresting them, but purely to mete out punsihment, then that is unlawful.

Then there are degrees of what is unreasonable.
For instance, chasing, or reacting to a criminal with a hand brush (as in the jewelry heist), is hardly going to be in the public interest to prosecute.
Chasing a criminal with a hammer, baseball bat or scaffold pole would merit more serious consideration.
And finally chasing someone with a firearm would undoubtedly result in a prosecution.