Some topical titles:
This is the first in a three book series which has the Queen assisting in investigations and was published in 1996.
The first in a series in which Her Majesty The Queen, with the help of housemaid, Jane Bee, investigates some mysterious murders at the royal residence. Jane believes her friend, Robin Tukes, a palace footman has been murdered - and so does a VIP who asks Jane to help her investigate.
This one's a bit older, coming out in 1981 and according to wikipedia: "purports to tell the story of a hushed-up murder in the Royal residence in 1935. Despite its including 'documentary' photographs, there is no external evidence that the book is anything but pure fiction."