Constitutionally, she has the power. It is highly doubtful, given today’s political climate, that she would take such a drastic step.
Unless she had no choice. The reserve powers do exist to deal with an actual breakdown of government. This is very unlikely to happen, largely because the powers exist. No government or opposition is likely to force the Queen to intervene.
After the last election, when Gordon Brown finally gave up on trying to hold onto government with a coalition, he phoned Nick Clegg to tell him the news. He said, according to news reports at the time:
"Nick, Nick. I can't hold on any longer. Nick. I've got to go to the palace. The country expects me to do that. I have to go. The Queen expects me to go. I can't hold on any longer."
The Queen expects me to go. That was the bottom line. He would not force her to intervene - no modern Prime Minister is ever likely to - but the fact that she can, is something that they have to consider, and take account of.