Does the UK prime minister have to answer to the Queen?

The Prime Minister of Canada is answerable to the Canadian House of Commons, which is composed of the elected representatives of the Canadian people.

Since it is ultimately the Governor General who has the power to dismiss the Prime Minister, in theory, the Prime Minister would be answerable to the Governor General. In practice, the Governor General is apolitical, and would only use this power to remove a Prime Minister who is abusing Parliament and refuses to resign.