I’ve “eaten” with the Queen ie within walking distance, but not exactly intimate, on several occasions - as a guest at a formal do. These sort of invites come along if you do the right sort of job (mine have usually come through the Queen’s Awards for Industry/Export - which is the line I’m in).
I have also been invited to Highrove a couple of times, which again is an occupational hazard (and the Prince Of Wales hits you for a “donation” to the Prince’s Trust).
HM the Queen has better food and is more generous with the wine.
Recently a tabloid reporter infiltrated the Place and exposed the thruth about how the queen dines when alone:
http://www.mirror.co.uk/news/allnews/page.cfm?objectid=13638235&method=full&siteid=50143