As a Brit I'm embarassed to say sometimes yes, I have met the Queen. I used to sell tickets to her properties, even went to tea with her in the palace (with 500 other people), and lavish Xmas parties in the thousand room castle, slapped in my home town. She opened my new school wing, our church extension, the local hospice, the local Xmas lights every year, involving tinsel around lamp posts, would see her driving her car down the street on Sundays (if you knew when and where to look), shook her hand about 5x. If you paved your back yard she'd be standing there bleary eyed with a pair of gold scissors. The princes would be in the local nightclubs and ex-strip joints like a rash.
As a polite reminder, there are near 70 million people in the UK, hardly anyone's ever even seen the Queen or her family. It's a bit like the chances of the population of the American West having met say Tom Hanks, since he lives in LA.
She is btw tiny, and has quite a sharp, modern sense of humour. The tabloids once caught a pic of her using the gold scissors as a slow, psycho style reenactment during a boring ceremony. She was at the time staring at the Pope. Can't find the pic, but somewhere, it's out there.