Gosh that's a complicated question.
The short answer is that no confidence votes are meant to be a way of taking the issue to the people for a general election, not replacing the governing party and its leader with a Prime Minister who's election by the people is unthinkable.

Neither Kenneth Clarke nor Harriet Harperson could imaginably be elected either to lead their respective parties or as Prime Minister, and could only possibly be Quislings to force through the will of a minority at home and the wishes of a foreign power.

If a vote of no confidence were successful then the one and only acceptable outcome in these circumstances is a General Election.
Any attempt to install a ridiculous candidate by a small clique of M.Ps would be nothing more than an attempted coup, and the Sovereign would be likely to refuse to sanction it and call a General Election herself.

As I said earlier though, I very much doubt that in the event they'd really attempt to go down that line.