It's main line down to Derby was closed and there were few enough lesser routes to be diverted to the other terminals. Would have been around 1967-68 ?
I travelled from Hartford and Greenbank (as it was then called) to Central daily throughout that era. The Miller's Dale line closed in mid 1968 but Central soldiered on for about a year until platform alterations at Oxford Rd. were completed. At that time there were no through passenger trains at Oxford Rd., both directions turned back there.
The last vestiges of the former grandiosity at Central was an advertising arch one passed under to reach the platform from which The Master Cutler left (London via Sheffield obviously).
It was not a happy time, Britain was clearly a country in industrial decline at every turn. Engineering companies were involved in takeovers and mergers with breath-taking frequency actively encouraged, unfortunately, by the misguided policies of the Wilson government. Investment in railways was just about non-existent and everyone expected the huge declines that indeed followed.
The Wilson government did a lot of good things for Britain, but somehow got the idea that the way to achieve world competitiveness in export industry was by creating merged companies "big enough to compete with the Americans". This may have been true for aircraft but it was totally the wrong policy for most industry. Vast amounts of expertise in electromechanical systems that could have been applied to robotics and machine tools were simply lost to the NIH attitudes of merged companies everywhere. The only really successful industries were the state owned energy industries. The 1970 collapse of Rolls-Royce was a watershed but the dark ages continued as industrial relations just got worse and worse for years.
Sorry about waffling on, I just got started and then got carried away.