Hi Mike,
Saw your email but thought it probably better to reply here. Some info and leads concerning records on your third list:
Squadronaires "The Man Who Came Around"
This is on Decca F-7480. The correct title is "The Man Who Comes Around" and the correct artist credit is "The Royal Air Force Dance Orchestra". The band were not formally known as The Squadronaires until after the war. It appears to be included on the Flapper CD "Hits of the Blitz", which is available on Amazon:
https://www.amazon.co.uk/Hits-Blitz-Various-Artists/dp/B000026N3I
Carroll Gibbons "Goodnight Again"
According to Rust & Forbes British Dance Band discography, this is on Columbia FB-2547, and has vocal by Anne Lenner. It appears to be on the Memory Lane CD MLMCD037 "The Voice of Anne Lenner: Volume 2", which can be ordered through Dave Cooper's website:
https://www.talking-shellac.com/british-dance-band-other-artist-cds
Phyllis Robins "Goodnight Children Everywhere"
The other side to this record (It's A Hap Hap Happy Day") is included on the 2019 Memory Lane CD MLMCD077 "Phyllis Robins: My Bluebird's Singing The Blues". It might be worth contacting Dave Cooper to see if he knows who provided the record.
Arthur Askey "Mister Brown of London Town"
UK release for this is HMV BD-951. Have you tried the Arthur Askey appreciation society?:
https://www.facebook.com/groups/133117033760155/
I'll keep an eye out for the others on my travels.
All the best,
Peter