You can make that an 3/4 victory for Blair.
But you're right. British politics do work differently.
The Prime Minister's party is in complete power. And a strong Prime Minister is in complete control of that power.
Witness M. Chretien in Canada. We don't like how he exercises his power, but he's wielding it pretty effectively.
Mr. Blair, just by the challenge to him, is seen as weakened.