IIRC, the Queen wanted to leave the EU and publically stated so.
She did not make a public declaration as you suggest, as that would have been seen as a violation of the traditions surrounding constitutional monarchies, where the monarch does not publicly 'take sides'.
Sh did make her preference known, however, by challenging some folks to "give me three good reasons to remain in the EU," at some official function. That comports with the tradition, as it isn't an outright endorsement of a position, while indicating a possible preference...
the infowarrior