The UK is not Canada though. You have the House of Lords, we have a Senate. We are a (con)federation, and that adds a whole new political overlay that the UK doesn’t have.
The executive power of our PM relative to the body politik is much higher. We don’t have a tradition of backbench rebellion, and the PMO often wields more power than the cabinet.
The point is that a parliamentary system doesn't need to mean an unchecked leader