Who has more power in the British government, the Queen or the Prime Minister?

In the
Constitutional system as it has evolved over the centuries, the monarch has come to have no
actual "power." The Queen now (or King when there is one in future) is the head of
state, but this is a symbolic role and carries no governing authority with it. The Prime
Minister, as head of government, is of course free to consult with the Queen, but the latter
explicitly is not permitted to have a direct role in government. The monarch, however, is the
head of the Church of England as well as head of state.

Note the difference
between the Parliamentary system that operates under the British Constitution and the division
of power prescribed in the US Constitution. In the US, the President is head of state, but the
government is spread over three branches of which the President is the executive, Congress the
legislative, and the Supreme Court the judicial. In Great Britain the elected party, of which
the Prime Minister is the head, holds the power of government in its Parliamentary majority. But
because the UK, like the US, is a democracy, there is always an Opposition in Parliament so that
all political parties of whatever orientation can be represented in the legislature, just as the
minority party holds seats in the US Congress.