I thought some of the forum members might find the following of interest. This was the explanation given to a lady from Huddersfield, England who had enquired as to the R.A.F. roundels. FYI this came from an English publication and was sent to me.

The origins of the Royal Air Force Roundel come from World War I, when there was a need to identify aircraft. The Union Flag was first painted on the under-side of the lower wings at the end of August 1914. This was satisfactory at low level but was confusing when the aircraft was higher as only the cross was visible, and this was often mistaken for the German cross. For this reason, in October, 1914, the system of concentric circles was adopted, though the Union Flag was retained in miniature between the circles and the wing tips.
This miniaturised Union Flag was also painted on the rudder but was replaced by red, white and blue stripes in May, 1915, and in June of the same year, the roundel was painted on the top surface of the upper wings. The Union Flag on the aircraft was abolished altogether.