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I was going to mention I remembered you worked on site.
Then I think your wording was a bit unclear, it read like you're talking about essential and non-essential work as policeable things (and that policing them would be impractical/undesirable), which they aren't really.
I agree, way too much pointing the finger at "non-essential work" when that's totally allowed. It's "essential" to travel to (non-essential) work if you can't work from home.
https://www.gov.uk/government/publications/coronavirus-outbreak-faqs-what-you-can-and-cant-do/coronavirus-outbreak-faqs-what-you-can-and-cant-do#how-can-i-find-out-if-my-work-is-essential-or-not
My point was that people have been pointing the finger at construction workers, as if there were a line to police, which is wrong, so we are in agreement here.
I work in construction, and felt very uncomfortable in the last week at the workshop leading up to lockdown. I was relieved when we closed even though I lost 6 months income. I was able to mitigate this hit, but I know many can't. My point is more about blame culture and finger pointing in the context of this government statement, than the practicalities of safe working environments.