On a recent visit to a REME training battalion, there was a mixture of beret's I noted but more the "Para Beret" that stood out most, in a conversation with one of the Ex Regs on the course, I was always under the assumption that many years ago that the Red (Maroon) Beret was only awarded after completion of P company and the required jumps, but also a soldier at the time could do the Parachute training without doing P company but was only issued the Para wings...
Only ask as there were a few with the "Red Beret" with no wings and others with wings and Beret...