I don't think it's quite fair to say the government doesn't believe it should be honoured. They have been trying to find a brexit arrangement that works, but have failed (miserably, in most estimations). But this was always going to be difficult when MPs have various ideas of what brexit should...
A vote for remain wouldn't have required 'enacting' because the status quo would have been maintained.
The issue with brexit is that no-one was asked what kind of brexit they wanted, hence the last three years.
I'm not advocating for the UK to remain, but if you do really believe in democracy...
I hate to be the one to tell you this, but I'm afraid a referendum (and indeed an election) is a poll.
YouGov don't have any agenda, as far as I'm aware, so I'm not sure how they would be 'leading' me. But do explain.
https://d25d2506sfb94s.cloudfront.net/cumulus_uploads/document/ojewuniikg/Internal_190401_BrexitTrackers_w.pdf
But even if there wasn't accurate polling, you would need to rerun the referendum because the result is outdated. As a democrat, I'm sure you agree.