Whilst I'm inclined to consider the Derbyshire police response as an attempt to make a strong and visible point (which may or may not be successfully challenged), I also think it's probably no bad thing that police forces come out strongly on this.
It certainly gets the message across loud and clear, and let's face it, it will probably take dare I say "heavy-handed" police responses such as this to force the public to think twice about whether driving out of your village/town is really acting in the spirit of the lockdown, irrespective of whether the legislation is ambiguous or undefined.
I'm starting to ask myself whether the AT has perhaps done more harm than good with their lobbying. It has given us an opportunity to give angling a bad name, such as in @Odyssey's recent example of someone driving from Exeter to Minehead. It'll only take a couple of high-profile instances of anglers being caught way out of their local area for public sentiment to turn against us and then the government will have to act to ban fishing again... and potentially take a more strict view of angling in future.