I sort of think they might be going that route. No sane person in their government wants to go through with this. If I'm understanding this right, they're on a course for a 'Hard Brexit' which would be an utter disaster. The longer they draw that out and the public sobers up the less of a political hit they'll take in just calling the whole thing off or postponing it indefinitely.
You are vastly overestimating the sobriety of the british public. The vote as it was was close (with far from a 100% turn-out), and given how many people voted for protest reasons beyond actually wanting it or were sold on lies who who didn't want a no-deal brexit... it's pretty much established that the number of people that want this is a minority, but enough fear and hatred has been stoked that there will be chaos from them if the government drags it out this long and then backs out.
As far as people in the government go, you're overestimating their sanity. Tories are led by Theresa May who got handed control of a burning car and decided what was really needed was gasoline, and the main opposition is currently led by Corbyn who's pretty much only in power because of a borderline cult of personality and had to kick out half of the party to keep power so he's hardly, well, opposing...
Add into that the BBC adopting the policy that brexit's a done deal and just straight-up not reporting on the controversies and opposition...
At this point what people are asking for is not cancellation, but rather a people's vote now that everyone's more informed about the consequences. Do they want a no-deal brexit, do they want a softer brexit and if so what deal, or do they want to stay?
That'd be the safe way out for them, especially given Farage (guy behind the first referendum) said he'd be campaigning for a second vote if it was as close as it was and he lost, but nope, they're apparently committed to disaster.
There's no way this doesn't end badly.