It was a big mass changeover in that June 1962 weekend, with a new timetable. Electric trains had made some infiltration beforehand, as much for crew training as anything, in fact they had been built a couple of years before, but had been used short term on the GE lines to help out with first the 1500v conversion and then the electrical failures that followed shortly afterwards.
The BR Standard 80xxx tank locos, unlike the 3-cylinder LMS ones, did indeed move on, many to the Western Region on the Cambrian and Central Wales lines; the WR had not had this class of locos before. They didn't last long there. Former LT&S locos were not normally welcomed at other depots as the water quality at Tilbury and Shoeburyness, despite extensive and necessary provision of water softening plants, was the worst on the whole of BR (well, somewhere had to be, and this was it), and the boilers suffered significantly, despite there being far more frequent washing out than elsewhere; I read that the steam loco fleet was about 15% higher than the average would expect, purely to cover so many washing out on any day.
That instant change is how it was often done at the time. The Glasgow Blue Trains did the same sudden switchover.