Oh dear! Just had a look at the Yahoo group thread, and found this:
As a homage to HM Queen Elizabeth II in her Jubilee year, I invite the motorcyclists amongst you to see another side of the Queen, doing her motorcycle test as HRH Princess Elizabeth with the ATS as a teenager during WW2. I saw this photo in a wartime motorcycle magazine amongst a load I bought in a junk shop and spent ages tracking down the archive. It was published again in the men's magazine Vogue Hommes International in 1998 and the Palace was most grateful to be in touch with the archivist who helped me find the original negatives as HM had no copies. We were told that she was very pleased to be able to show the picture to her grandchildren. The bike is a 250cc sidevalve BSA C10.