Of course, as you already are aware, the United Kingdom is a Constitutional Monarchy. Her Majesty Queen Elizabeth II, Queen of the United Kingdom and the other Commonwealth Realms is the Head of State, and the Prime Minister (currently David Cameron) serves as Head of Government.
Unlike other Commonwealth Realms, such as Australia (with the Australia Act 1986) and Canada (with the Canada Act 1982), the United Kingdom still has the 'royal prerogative'. The royal prerogative is the customary authority and privilege recognized in the United Kingdom as the sole prerogative of the Sovereign (i.e. QE II). This prerogative extends to defence, foreign affairs and national security.
However, since the 19th century, by convention, this prerogative is no longer exercised by the monarch acting on his or her own initiative. Now, the advice of the Prime Minister or the Cabinet - who are then accountable to Parliament for the decision - has been required in order for the prerogative to be exercised.
This being said, the Monarch still remains constitutionally empowered to exercise the royal prerogative against the advice of the Prime Minister or the Cabinet, but in practice would only do so in emergencies or where existing precedent does not adequately apply to the circumstances in question.
So, where does that leave us? Essentially, the Prime Minister can order the firing of the UK's nuclear weapons, and, without the approval of Parliament, send the country to war and make peace. However, it is unlikely he/she would do so without consulting with the Queen, who is currently kept 'in the loop' with government affairs by way of a weekly audience with the Prime Minister.
Leyland best sums up the case surrounding this issue in saying:
"[But it] should be emphasised that the prime minister is not under any obligation to take account of royal opinions."
Summary: The PM and Cabinet make the decisions. They keep the Queen in the loop. She can reject the decision made by the PM and Cabinet under her royal prerogative. In this case, it is uncertain what would occur.