I didn’t know the monarch had any power left.
They are referred to as the reserve powers.
They include:
The power to refuse to resolve Parliament on the request of the Prime Minister. This last came close to happening in 1910, but Edward Heath specifically asked the Queen for her assurance she would grant him an election if asked as late as 1974 (when he agreed to take office as head of a minority government).
To appoint a Prime Minister of their own choosing. The Queen did this in 1963 after the conservative Prime Minister Harold Macmillan resigned from office on the grounds of ill health and it emerged that the Conservative Party had no mechanism to replace a Prime Minister who had resigned - she agreed to use her power to do so, but told them to come up with a procedure to avoid it happening again.
To refuse the Queen's Consent to allow laws on a very limited number of subjects to be debated in Parliament. The Queen did this in 1999 (the last time she exercised any of her powers) to prevent debate on a law that would have given Parliament the power to authorise military strikes on Iraq without the Monarch's consent - she did this at the request of the government of the day that didn't want the change (it was proposed by a group on the extreme left of the Labour Party and was opposed by both the Labour government and the Conservative opposition so had no hope of passing and would have just wasted Parliament's time).
There are other powers but they either haven't been used for so long, they are considered largely dead, or they just relate to formalities that aren't that important.
In the type of situation being discussed here - if a government ignored a referendum, the Queen's right to appoint a Prime Minister of her own choosing and/or to dismiss a government from office and call a general election would become relevant as the Queen would be entitled to act to ensure Parliament respected the will of the people.
While no Monarch has had to do this in the UK since 1834, it has been done by the Queen's representative in Her overseas Realms - it happened in Australia in 1975 when the Governor-General Sir John Kerr, dismissed Prime Minister Gough Whitlam and his entire government from office, after Whitlam could not present a legal plan to continue governing without a budget, and refused to ask for an election. The powers are real - but a competent government would not make the Queen use them.
If you go back to the British election of 2010 which resulted in a hung Parliament, you might remember that there was a period in which Prime Minister Gordon Brown was trying to stay in office by making a deal with the Liberal Democrats. When he finally gave up, he is known to have told the Liberal Democrat leader that the Queen had made it clear he'd run out of time - she'd given him the chance to make a deal if he could, but in the end, while she didn't step in, she told him that he knew what decision he had to make. And being a good Prime Minister who respected the way things are, he did the right thing, rather than force her to intervene. It's very unlikely any Prime Minister will ever force the issue.
(The fundamental control on the Queen's powers is that the last time a Monarch abused them and went too far, he had his head chopped off - the Monarch understands that the British people will only accept the use of these powers to protect the Constitutional integrity of the United Kingdom and abusing them would bring down the Monarch and possibly the entire Monarchy. But the powers are there for resolve an actual constitutional crisis.)