Actually there are two types of VoNC that are relevant here. Parliament could express their lack of confidence in Boris Johnson himself, rather than the entire government. The constitutional expectation, if such a motion passed, would be that the Conservatives put forward a leader to take his place.
Expressing no confidence in the entire government is the more extreme (but more common) course of action. The recent precedent is Jeremy Corbyn requesting (but being denied) the opportunity for the HoC to carry out a VoNC targeting Theresa May in 2018, although it required time in the Commons which the government refused to grant him.
The BBC said[0] at the time:
> Unlike a vote targeting the PM, a motion of no confidence in the government could bring about an early general election if it is supported by a majority of MPs.
and it was later, in 2019, that such a VoNC in the government itself went ahead.[1] Theresa May won that motion by 325 votes to 306.
[0] https://www.bbc.com/news/uk-politics-46599895
[1] https://en.wikipedia.org/wiki/2019_vote_of_confidence_in_the...
So the only way to remove him of he won't quit is a House of Commons vote of no confidence.
But that, by convention, means a general election.
And a lot of the conservatives that would have to vote for it would almost certainly lose their seats since they only won them narrowly and the polls show they're down.
So unless MPs put aside their own interests and act in the national and democratic good, we'll likely be stuck with Boris?