There's no systematic way to find out which vinyl recordings were re-released on CD, but it's often possible to find out with a bit of detective work.
Taking the example from the question, the LP has two works by Benjamin Britten conducting the London Symphony Orchestra and was released by Decca in 1964, so it's likely that all of it was recorded in the same series of sessions in 1963-1964. The two works probably ended up on two different master tapes. Since the soloist on the Serenade is Peter Pears, Britten's partner and dedicatee of the piece, it's probable that this was intended to be the 'definitive' version.
With the advent of the CD in the 1980s record companies starting producing new all digital recordings of works in their catalogs for their expensive new releases and re-releasing older recordings on their 'budget' CD, often in other combinations and often compilations. Those are the places to look for re-releases of older recordings. In general, if a recording has the same conductor, orchestra, soloists, producer and recording (not release) date and a similar running time, it's most likely a re-release. Decca – 417 153-2 DH is probably one example of a CD re-release of the Serenade coupled with two other Britten works.. The second piece from the original LP "The Young Person's Guide to the Orchestra" might have been re-released somewhere else. These older recordings also often turn up on streaming sevices, or as digital downkloads.
In rare cases a record company will get all participants back into the studio at a much later date, to re-record a piece using the newest technology, but they couldn't have for these recordings: Britten died in 1976. One example is Glenn Gould who recorded Bach's Goldberg Variations in 1955 and again digitally in 1981. Nikolaus Harnoncourt recorded Bach's Brandenburg Concertos with the Concentus Musicus Wien in 1964 and again digitally in 1981. Collectors still prefer the older recordings in each case.
Recordings that the record companies didn't find 'good enough', often disappeared into their archives and never made it onto CD.