My closest encounter with the Queen was during her visit to the Commonwealth games, Christchurch NZ, in 1974.
Her Majesty was given a royal tour of the recently completed student halls of residents, where I was accommodated. A fellow student and I thought it would be a lark to cycle out from a lane between the buildings as she passed. We managed to position ourselves between the Royal car and the following security detail, pedalled along within the Royal convoy for 50 yards or so. Many years later, I happened to meet the officer in charge of security for the Royal visit, for which he had been knighted. I did not rain on his parade and was glad not to have come any closer to him at the time.