Steve: "We're told that almost no-one wants no-deal"

That's the problem. Some people just believe what they are told.
When Cameron suggested a referendum I'm sure he was told Remain would win it. People on this site seemed to think it was a forgone conclusion. The reality was something different.

If you were to say that "very few MPs want no-deal" then you may well be correct. But the majority of MPs (apparently) favoured Remain anyway, so that would not stretch credibility.
What the people of the country want in the current situation has yet to be tested, but the latest referendum is still the 2016 one, and a majority (of those who voted) voted to leave the EU.