I have come across a few San-Remo's and other Falcon's in my time. The San-Remo trademark was the wrap-over seat stay, my mid 70's San Remo has seat stays just like yours but with long point prugnat lugs. Falcon's of that era always had quite a bit of chrome which may be covered by green paint.
They seemed to put the frame number wherever they liked, bottom bracket, seat tube behind the seat, seat tube up from the bottom bracket, rear dropout and even stamped into one on the chain stays underneath. Should also be a number on the steerer.
Falcon's always rode well
Typical Falcon lack of anything brazed on as well. Very nice frame, should re-finish well as they paid attention to the lugwork as it was often chromed.