That’s just silly pedantry. Do you really think that when someone refers to their MP, as in “I’ve asked my MP to help with this issue”, that someone might think they mean the Queen, or Governor General, or a Senator?
Whereas to me, “Congressman” really is inherently ambiguous, though I recognize its widespread use to mean a member of the US House of Representatives. Because if someone is a man, and a member of the US Senate, they are also by definition a “Congress man”.