I think Beeching would never have been able to totally gut the UK system as the UK rail system never fell into the type of marginal insignificant role that the US system outside of the NEC did. Even in the darkest years, there was a considerable and consistent system-wide ridership on BR that could not easily have been absorbed by the roads. In many cases rail was also considerably faster and more comfortable than driving, and large cities, especially London, were even then heavily afflicted by congestion meaning that closing the commuter lines was simply unthinkable.
Beeching reduced the system mileage of BR by about half, but reduced passenger miles by only a fraction of that. Many of the lines he closed were extremely marginal or indeed duplications of other routes and would sooner or later have had to close anyway. France and Germany have seen their systems shrink by a similar amount (if not more) but over a longer period of time. So what Beeching essentially did was apply a shock therapy that permitted BR to concentrate on the routes where it mattered. It was of course a huge and regrettable waste that this came so shortly after the modernization plan with lots of near new equipment becoming surplus and having to be written off.
In terms of the freight network, Beeching reduced this by more than the passenger network, but also managed to reorganize the rather backward and slow system and create profitable corridors, as well as accelerate the introduction of things like intermodal services.