I'm no music expert but I felt the musical arrangements were too "modern" for the era.
The name Leslie Hutchinson has been mentioned as the basis for the 'Louis' character.
This is him performing in 1933
This is the sort of music that cafe society was listening to.
Yes, I said the same thing earlier in the thread with a link to Hutch's "These Foolish things."
The exception was probably "Hutch" (Leslie Hutchinson), a cabaret pianist/singer the only name I can think of who was black and very popular with society in those days. Often featured on the radio.
I think what the the producers have done, is instead of getting the band to play in the style of what would have been played by Afro/American bands popular in the States around that time, (see my previous link to Fletcher Henderson)........
they've chosen the timeless sound of the most popular "big band era" from early forties to late fifties, these band would have consisted of as many white as black musicians.
The Fletcher Henderson band now sounds very dated and might be a turn off for viewers of what is principally a drama with some music,
If there had been a band that played like the one depicted in the programme, the jazz enthusiasts on here would have known about it.