The classic design assigns making law, executing law and judging disputes to different institutions, each checking the others. The United States built the strictest version: a president who cannot sit in Congress, a Congress that cannot dismiss him, and courts independent of both.
Westminster systems fuse the first two branches — the executive is drawn from, and survives at the pleasure of, the legislature — so their separation of powers is really about the third. What the tradition insists on everywhere is the independence of the judiciary from both political branches.
Canada fuses executive and legislature in the Westminster way, but the Supreme Court has treated the independence of the courts — anchored in ss. 96–101 of the Constitution Act, 1867 — as a constitutional principle no government can override.