The end result may still be largely the same over the course of time, if not as singularly defining under the Beeching name as it became. If it happens in dribs and drabs anyway, it could impact the wider modernisation efforts and thinking as well. There would also not be the "Beeching bogey-man" mythos of OTL.
On the other hand you might have a more balanced mixture of modernisation of infrastructure with fewer outright closures spread out. But the trouble is, there's going to be big changes happening as the governments of the day needs to cut expenditure somehow. Without some form of closures in the mid 60s, the entire network runs the risk of complete, eventual collapse where basic functionality is literally. Think what happened with Penn Central...