The Queen has power over the calling and dissolution of parliament, and of the appointment of Prime Ministers. She is also head of the Military, and has the power to declare and conduct wars.
She can veto any law, but in practice only vetoes laws that relate to her own powers.
She is also Head of the Church.
She has no tax-raising powers though, which means she cannot really operate independently.
From the Glorious Revolution onwards, Monarchs' power was really only two things: appointing Prime Ministers, and vetoing bills related to their own areas of power.
However, the Queen discovered that she really wasn't much good at choosing Prime Ministers, as she was manipulated by politicians (she was quite young at this point). Also, the collapse of the Liberal Party meant that parliamentary politics were much simpler: either Labour won, and they chose their own leaders, or the Conservatives won. In 1963 she chose a Tory leader, after a big scandal under the old one involving a prostitute, but he didn't really do very well. After that, the Tories elected their own leaders.
Because now one or the other party has a majority, there is no practical choice other than the leader of the biggest party, so she always chooses them.

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... I am surprised at your insolence in writing to me at all. You know, as I know, that I bought this constituency... may God's curse light upon you and may it make your women as open and as free to the excise officers as your wives and daughters have always been to me while I have represented your scoundrel corporation.
I have the honour to be... your obliged humble servant, Anthony Henley
- MPs reply to constituent, mid 1700s