Thanks, Gannett2017. I can identify two more of the tracks:

15:55 Golden Melody (Peter Yorke), 1956
23:16 Adios Mexico (José Payan/Fred Hartley), 1955

I have been unable to identify the truncated track that begins at 18:43.

0:00 - 'Bicycle Belles' by Sidney Torch (1956) - Chappell Recorded Music - C.531
2:41 - 'Barbarina' [also misidentified as 'Babarina'] by Bruce Campbell (1958) - Chappell Recorded Music - C.500
5:02 - 'Swing-Hoe' by Robert Farnon (1954) - Chappell Recorded Music - C.459
7:33 - 'Invitation Waltz' by Richard Addinsell (~1949) - Chappell Recorded Music - C.378
10:31 - 'Blue Mink' by Peter Yorke (1953) - Chappell Recorded Music - C.466
12:58 - 'Seventh Heaven' by Robert Farnon (1952) - Chappell Recorded Music - C.410
15:55 - ?
18:43 - ?
20:24 - 'African Moon' by Robert Stolz (1959) - Chappell Recorded Music - C.616
23:16 - ?
25:55 - 'Hi-Fi Polka' by George Blackmore/Frank Naylor as Michael Summers/Lou Rogers (1961) - Chappell Recorded Music - C.711