The dive-under was built as part of the scheme between 1900 - 1905 to increase track capacity in the Sheffield area. The original double track between Sheffield and Dore & Totley was increased to four, with new lines being built on the east side of the originals. At the same time, Sheffield station was extended and rebuilt to provide a new frontage on to Pond Street and additional platform capacity. Manchester traffic was to be allocated mainly to the original lines towards Dore & Totley and London traffic to the new lines. To bring the Down Fast line across to the west of the station (the Platform 1 side), a dive-under was built between Queens Road and Sheffield South No.1 boxes.
The new lines were brought into use at the end of October 1901. Paradoxically, the old pair of lines, now the Manchester lines, were designated the fast lines and the new pair, the Chesterfield lines, became the slow line. This was not changed until 1954, when the designations were reversed. Whilst the widening of the running lines from Dore was on the east side, the expansion of Sheffield station (construction of platforms 1 and 2) was on the west side, so the diveunder was provided to bring the overwhelming majority of the longer and heavier trains from the south into the new "Hausbahnsteig" with no conflict with the down Manchester line. So the layout ended up with the Manchester lines running into the new island platform 2/5 and merging with the Chesterfield lines at the north end (pending the widening there that was planned but never done) and the London lines serving platforms 1, 6, and 8.
The original Sheffield layout had what is now the platform 5 line as the "Hausbahnsteig", then a pair of through lines (which were changed early on to sidings) and the platform 6 line as tghe up platform line. Behind the station was a pair of goods lines, the up goods largely on the site of the present platform 8 line, the only trace of the down goods being the site of what later became the bay platform line set into the north end of platform 8.
Those were still the days when the major companies were planning and building generous layouts for the easy handling of future traffic, not layouts pared back to an absolute minimum in an expectation that everything would always work perfectly and there would be no growth, like the Ordsall Chord / Castlefield Corridor set-up in Manchester today.