BSA Bantam D7 in Movies
The BSA Bantam D7 is a single cylinder, two-stroke allround motorcycle produced between 1959 and 1966.
Drive
The bike has a 3-speed transmission.
Chassis
Stopping was achieved via expanding brake (drum brake) in the front and a expanding brake (drum brake) in the rear.

Under Suspicion
Looking for the bike. BSA Bantam D7 circa.1965 (..I had one of these.! ..but mine was metalic blue.!) 175cc ..with a massive 7 bhp.! What a racer! With your info I found a nice page about the Bantams: http://www.bantam.150m.com/history/index.html According to this source the D7 started in 1959 which would fit to the film scene. I don't believe the earlier models had metallic paint or chromed fuel tank..?
that's true, the jelly mould tank came in 1965. My D7 is a 1962 and has a jelly mould fitted,