Actually, Jane, I can confirm that the Queen does indeed go to the toilet. In the 60's I was part of a team doing restoration work in Holyrood Palace in Edinburgh, and part of this work involved repairs in the Royal bedchamber.

The Queen and Duke had separate sleeping quarters as I recollect, and I distinctly remember the ensuite toilet arrangements in Her Majesty's room. All the ceramics were white, (no pink or avocado), and the flush in the WC was operated by a foot control, which was pretty avant garde for the sixties. I was rather surprised to note that there was no bidet, however ....

Murray