You could try sending a message to EMI Archive Trust to ask about their 78rpm transfer service. I couldn't get the form to send, but the email address is info@emiarchivetrust.org.


The following are held by King's College Sound Archive in London (based purely on a listing I have of just the catalogue numbers)... although they were quoting me £20 per side transferred last time I asked. I've asked my contact there if they are still doing transfers.

2….Goodnight Children Everywhere – Issy Bonn HMV BD 797
3….My Favourite Dream – Turner Layton Columbia FB 3080
4….My Daddy – Phyllis Robins Parlophone F 1703 ************* (3 copies apparently)
5….Dreaming – Beryl Davis Decca F 7472 *************
6….If Tears Could Bring You Back – The Organ, The Dance Band & Me Parlophone F 1786 *********
7.....I Hear A Rhapsody – Turner Layton Columbia FB 2666
8.....What Do We Care – Billy Cotton & His Band Rex R 10023
10...Do You Care – Geraldo & His Orchestra Parlophone F 1889 *************
11…By Candlelight – Turner Layton Columbia FB 2771 *************
12…You Are My Sunshine – Billy Cotton & His Band Rex R 10115
13…I Don’t Want To Walk Without You – Joe Loss & His Orchestra HMV BD 5742
14…Let The Rest Of The World Go By -Joe Loss & His Orchestra HMV BD 5905
15…Under The Willow Tree – Harry Roy & His Band Parlophone F 2107
16.. .You Walk By – Joe Loss & His Orchestra HMV BD 5778
18.. ..Praise The Lord & Pass The Ammunition Columbia FB 2887 [artist?]
19.. ..Daybreak – Turner Layton Columbia FB 2886
20.. ..I’m Thinking Tonight Of My Blue Eyes – Jay Wilbur & His Band Rex R 10187
21….Heavenly Music – Turner Layton Columbia FB 2973
22….Shine On Victory Moon – Carroll Gibbons & His Orchestra Columbia FB 3069
23….I’m Sending My Blessings – Turner Layton Columbia FB 3009
24….Don’t Ask Me Why – Joe Loss & His Orchestra HMV BD 5838
25….Thinking About The Wabash – Joe Loss & His Orc. HMV BD 5838
26….Silent Night – Pat McCormac [typo - McCormack] HMV BD 1119
27….Long Ago & Far Away – Turner Layton Columbia FB 3035
28….Someday I’ll Meet You Again – Carroll Gibbons & His Orchestra Columbia FB 3038
29….Spring Will Be A Little Late This Year – Turner Layton Columbia FB 3058
30….Spring Will Be A Little Late This Year – Ambrose & His Orchestra Decca F 8450
31….My Favourite Dream – Billy Cotton & His Band Rex R 10127
32….My Favourite Dream – Eric Winstone HMV BD 5869
33….Together – Turner Layton Columbia FB 3100
34….A Friend Of Yours – Joe Loss & His Orchestra HMV BD 5895
35….Just A Prayer Away – Joe Loss & His Orchestra HMV BD 5895
36…..I’m Always Chasing Rainbows – Turner Layton Columbia FB 3201
37…..Carolina – Billy Cotton & His Band Rex R 10230

The British Library have these:
3….My Favourite Dream – Turner Layton Columbia FB 3080
7.....I Hear A Rhapsody – Turner Layton Columbia FB 2666
9 ….My Sister & I – Royal Air Force Dance Orchestra Decca F 7984
10...Do You Care – Geraldo & His Orchestra Parlophone F 1889 *************
11…By Candlelight – Turner Layton Columbia FB 2771 *************
14…Let The Rest Of The World Go By -Joe Loss & His Orchestra HMV BD 5905
15…Under The Willow Tree – Harry Roy & His Band Parlophone F 2107
16.. .You Walk By – Joe Loss & His Orchestra HMV BD 5778
18.. ..Praise The Lord & Pass The Ammunition [Carroll Gibbons] Columbia FB 2887
19.. ..Daybreak – Turner Layton Columbia FB 2886
22….Shine On Victory Moon – Carroll Gibbons & His Orchestra Columbia FB 3069
23….I’m Sending My Blessings – Turner Layton Columbia FB 3009
26….Silent Night – Pat McCormack HMV BD 1119
27….Long Ago & Far Away – Turner Layton Columbia FB 3035
28….Someday I’ll Meet You Again – Carroll Gibbons & His Orchestra Columbia FB 3038
29….Spring Will Be A Little Late This Year – Turner Layton Columbia FB 3058
30….Spring Will Be A Little Late This Year – Ambrose & His Orchestra Decca F 8450
31….My Favourite Dream – Billy Cotton & His Band Rex R 10127
32….My Favourite Dream – Eric Winstone HMV BD 5869
33….Together – Turner Layton Columbia FB 3100
34….A Friend Of Yours – Joe Loss & His Orchestra HMV BD 5895
35….Just A Prayer Away – Joe Loss & His Orchestra HMV BD 5895
36…..I’m Always Chasing Rainbows – Turner Layton Columbia FB 3201
37…..Carolina – Billy Cotton & His Band Rex R 10230

They also have HMV DB 5838... but could that be a typo, since there was no DB series, as far as I know? So maybe they have these two:
24….Don’t Ask Me Why – Joe Loss & His Orchestra HMV BD 5838
25….Thinking About The Wabash – Joe Loss & His Orc. HMV BD 5838

How to request a copy of a sound recording - British Library