It was almost always to save money in the short to medium term. BR was under intense cash pressure, and had what today would be called ‘unconventional’ methods of accounting. When stretches of track came up for renewal, it was (obviously) cheaper to lift one and not have to put it back. The signalling alterations were almost done for ‘free’ as design was counted as a overhead, and the implementation was often done by the local chaps, mostly in spare time. The maintenance savings came through immediately, as it halved patrolling costs, which is the main maintenance cost on lightly used lines. The fact that traffic ’doubled’ on the remaining track rarely affected that, as even with the doubling the traffic was below the threshold for raising patrolling levels. And, often, the service was reduced at the same time anyway.
Now you can say it was short termist, but how short term is short term? Some of the singling was done well over 50 years ago, and has saved at least two renewal cycles. Whilst some of the singlings have had to be undone in the last 20 years, it is pretty plain that the majority of them have not needed to be done and the savings continue.
Final point - sometimes the singling was done to make electrification cheaper. I have a feeling that some of the Kings Lynn line was singled at electrification - that’s 27 years ago now.