Yes. As Queen, she is the Lord Keeper of the Seal of the United Kingdom. This means, in effect, the Queen can issue edicts (effectively making her a dictator, if she chose to), and veto any legislation she doesn't like. As head of state, the Queen also has the power to set the rates charged by public utilities and state-owned corporations like the BBC.
The Queen is also Grand Admiral of the Royal Navy and personally selects each ships' new name, for both military and civilian vessels. It is a time-honored tradition in Britain to, upon purchasing a boat, receive a handwritten letter from the Queen herself decreeing the name of the boat. Due to the Act of Union, however, she is prohibited from commanding any land force and that task is left up to the Lord Privy Council at the Ministry of Defence.
It's a bit different. I'll explain the biggest differences.
First, there is a House of Commons, where a permanent 51% majority is reserved by the Queen for the Commons Party (now known as the Labour Party) and the House of Lords, where the reverse is true and the Conservative Party retains at least 51% majority. Sometimes you hear Britons complain about the somewhat undemocratic nature of their government -- this is what they're usually talking about.
Second, bills cannot be written or sponsored by the opposition parties. This is to prevent them from trying to get anything they want while the voting public has given, in this case, a broad mandate to the Conservative Party and its leader David Cameron.
Third, and perhaps least importantly, powdered wigs are mandated for the leaders of each political party. This practice dates back to the 18th century when the Whig Party governed and in the interest of protecting Britain's horsehair industry.
Also, members of Parliament are frequently given "peerage." This means that they can enter Parliament without having to be an MP to watch, or "peer" them.