Thank you. I see their story was posted about 45 minutes after my search. This is a sad day. I am disappointed in Liz. She may not have any political power, but she certainly has influence. I imagine she wished to avoid having her own children's messy divorces held up for ridicule again. So disappointed in her and Charles for that mess.
Yes, but constitutionally, she can only exercise influence over her Prime Minister and her government in private. She cannot do so in public.
The formula used to describe the situation is that the Queen has the right to be informed, to be consulted, to encourage, and to warn the Prime Minister in private on all laws. They have a weekly meeting expressly for this purpose which is completely private. During that meeting she is allowed to - in fact is supposed to - counsel the Prime Minister and tell him if she believes a law is a bad idea, and he or she is required to listen to her and consider what she has said. But the Prime Minister makes the decisions.
Prime Ministers have modified their policies in the past, apparently based on such meetings. But if they choose not to, that is their right. And the Queen cannot gainsay them in public. They are Her Majesty's Government - constitutionally a situation would be intolerable if the Queen campaigned against government policy. And constitutionally, ultimate power over legislation rests with Parliament not the Queen. Except on a very small number of constitutional matters. The Queen does have real power - but only in cases where Parliament can't do something (for example, if Parliament can't clearly choose a Prime Minister, the Queen would do so - and has used this power, twice).