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| Band Code | Title | Recording Date | Record Number | Vocal/Others |
| JHO | Hallelujah | 15/08/27 | HMV B-5332 | unknown vocals |
| JHO | Hallelujah! I'm A Tramp | 14/03/33 | Decca F-3573 | Pat O'Malley |
| JHO | Handsome Gigolo (Just A Gigolo) | 10/05/30 | HMV C-1970 | Pat O'Malley, Billy Ternent, Chappie d'Amato |
| JHO | Hang On To Me | 03/01/30 | HMV B-5759 | Pat O'Malley |
| JHO | Happy As The Day Is Long | 06/10/33 | Decca F-3671 | Jack Hylton, Billy Ternent, Pat O'Malley |
| JHO | Happy Days Are Here Again | 30/01/30 | HMV B-5771 | unknown trio |
| JHO | Happy Feet | 09/05/30 | HMV B-5843 | unknown trio |
| JHO | Happy-Go-Lucky You (And Broken-Hearted Me) | 24/08/32 | Decca F-3111 | Pat O'Malley |
| JHO | Harmonica Harry | 16/07/30 | HMV B-5875 | Pat O'Malley and trio |
| JHO | Have You Ever Been Lonely ? | 09/02/33 | Decca F-3476 | Pat O'Malley |
| JHO | Have You Met Miss Jones ? | 08/11/39 | HMV BD-5529 | Sam Browne |
| JHO | Haw Haw | 01/12/39 | HMV BD-5549 | Arthur Askey |
| JHO | He Played His Ukulele As The Ship Went Down (parts 1, 2) | 30/01/32 | Decca F-2798 | Leslie Sarony |
| JHO | Henry VIII Dances No. 1 - "Morris Dance" | 03/10/38 | HMV BD-606 | |
| JHO | Herr Lehmann, Herr Lehmann, Was Maccht Die Frau Gemahlin in Marienbad? | 21/05/30 | Electrola EG-1996 | Unknown Vocal |
| JHO | He Went In Like A Lion | 28/03/36 | HMV BD-5055 | unknown vocal |
| JHO | Heartaches | 02/11/31 | Decca F-2665 | Pat O'Malley |
| JHO | Heaven Will Be Heavenly | 1939 | film "Band Waggon" | Pat Kirkwood |
| JHO | Henry's Made A Lady Out Of Lizzie | 11/05/28 | HMV B-5485 | unknown vocal |
| JHO | Here Am I, Broken Hearted | 16/09/27 | HMV B-5360 | Jack Hylton, Jack Jackson, Billy Ternent |
| JHO | Here Comes Emily Brown | 03/06/30 | HMV B-5850 | Pat O'Malley |
| JHO | Heut' war ich bei der Frieda | 26/01/28 | Electrola EG-782 | Austin Egen |
| JHO | High And Low | 08/11/29 | HMV B-5772 | Sam Browne |
| JHO | High Up On The Hilltop | 29/11/28 | HMV B-5575 | Sam Browne |
| JHO | Himazas | 15/08/27 | HMV B-5321 | unknown vocal |
| JHO | Hold Me | 30/06/33 | Decca F-3600 | Pat O'Malley |
| JHO | Hold Tight | 14/04/39 | HMV BD-5475 | Primrose Orrock |
| JHO | Honey | 17/06/29 | HMV B-5663 | Sam Browne |
| JHO | Honeymoon Hotel | 18/11/33 | Decca F-3806 | Pat O'Malley, Sonny Farrar, Billy Ternent |
| JHO | How Are You ? | 04/10/32 | Decca F-3204 | Pat O'Malley, George Formby, Philippe Brun |
| JHO | How Long Has This Been Going On ? | 11/05/28 | HMV B-5485 | Jack Jackson, Billy Ternent, Chappie d'Amato |
| JHO | Hylton Medley | 02/10/25 | HMV B-2143 | none |
| JHO | Hylton Stomp | 12/10/32 | Decca F-3239 | none |
| JHO | Hypnotised | 14/02/36 | HMV BD-5034 | Ronnie Hill |
| JHO | H'lo Baby | 14/02/30 | HMV B-5788 | Pat O'Malley |