Your clever point would be cleverer if during that period London and the South East had no public transport improvements. No Thameslink (both versions), no DLR, no London Overground, no Croydon Tramlink, limited capacity, frequency and stock improvements to the National Rail network, no Jubilee line extension, no Heathrow line, no Paddington and King's Cross electrification, no Travelcard system, no Oyster system and no Contactless payment.
Meanwhile in Sheffield there's been the tram.
The posts that I am replying to relate to rail projects in Sheffield vs London and the south-east. Given that London rail travel represents about 2/3 of all mainline rail travel in the UK, whereas Sheffield would be somewhat less. In the absence of any data which is probably commercially sensitive anyway, lets's base it on the published number of exits and entries at the main station there compare with the numbers at the London main stations affected by the projects that you mentioned.
Sheffield - 9.6m
National Rail passengers on new and improved lines:
City Thameslink - 6.3m
Blackfriars - 10.5m
London Bridge - 48m
St Pancras International - 17+m (50% of domestic total)
Farringdon - 5m (40% of LU+TL total)
total passenger estimate /year at TL core stations = 80.5m
total TL cost including suitable trains = £6.5bn
GWR Electrification
Paddington - 36m
ECML electrification, (including Doncaster, Leeds etc.)
Kings Cross - 34m
London Overground, no costs available but it represents a ridership of 189m per year and serves 112 stations. Despite the very large size, it was really a project to tart up many poorly maintained lines and replace a mixed bag of life-expired trains. I suspect that the total stock of trains (124) will have cost less than £1bn.
The DLR has 45 stations and an annual ridership of 112m.
Croydon Tramlimk is smaller than Sheffield Supertram
The Heathrow line and its electrification was funded by Heathrow Airport owners (BAA at the time)
Crossrail was 2/3 funded from Greater London Authority and London business contributions
South Yorks has had day travelcards for years (I've used them myself), Oyster (or equivalent touch cards, not enough in Sheffield to justify a dedicated system by itself but ITSO cards are being introduced across the country by some TOCs, similarly, contactless payment could be introduced if there was a sufficient demand.
There's no really practical way to compare a large regional transport system as found in a world city like London with a relatively small city like Sheffield. Depending on whichever convenient method one might use to justify a city's ranking, (Sheffield can be the 6th 7th ot 10th largest city/metropolitan area in the UK), simply counting the number of people living within the city council's area is totally irrelevant when considering the provision of travel infrastructure and services. See this article:
https://www.citymetric.com/skylines/where-are-largest-cities-britain-1404