Popular music shows were rarely recorded and kept. With orchestras on
hand, the performances were often live and recordings for repeats were
destroyed after transmission because of copyright restrictions (they
were 'deemed' not to exist).
There are commercial recordings of music from that era, but the
repertoire is fairly limited. It was much more common for a popular
tune to be played by many different orchestras, each with their own
distinctive style, so the BBC could broadcast considerable variety with
only a small repertoire of tunes. A commercial recording represented a
significant investment for a record company, so they would only record
one version of the tune (or at most two) by whichever orchestra they
already had under contract, that they thought was best suited to it.
A significant proportion of the early editions of the BBC training
handbook "The Technique of the Sound Studio" by Alec Nisbett and BBC
training notes for Studio Managers is given over to microphone placement
for recording solo instruments, small combinations of instruments and
light orchestras for popular music. It was a normal bread-and-butter
thing to book a studio, a small band or orchestra, a soloist and an
announcer* to produce a 'live' half-hour light music programme; very
rarely was there any need to record one.
The best source of recordings would be transcription discs for
distribution to overseas transmitting staions and military bases, but
there were often destroyed after they had served their purpose. A lot
of the surviving ones are in bad condition and the equipment to play
them properly is very specialised because they were not recorded to RIAA
standards. A lot of American material of this type has survived, but
relatively little British.
*...and of course, a Studio Engineer, but nobody was concerned about
them.