She is supposed to be above politics, be neutral and not use her power to influence public opinion.
The Sun's claim stems from its initial claim from March.
So twice The Sun claimed that The Queen wanted Brexit. The Daily Telegraph also reported on a story which implied The Queen supported Brexit.
The Guardian was a bit pissed off about this:
The Sun was rapped over the knuckles for its “Queen backs Brexit” headline. Now, on the eve of the EU referendum, it has dared to feature the monarch on its front page again as part of its support for the leave campaign.
Its headline, “What the Queen asked dinner guests: Give me three good reasons to stay in Europe”, is based a revelation by royal biographer Robert Lacey.
[source : The Sun dares to use the Queen again in Brexit front page, The Guardian, http://www.theguardian.com/media/2016/jun/22/the-sun-queen-brexit-front-page, 22nd June 2016]
But if The Sun is so wrong then why has she not taken The Sun to court?