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And AFAIK the DLR reuses one of the routes of those lines on its way from
poplar to straford and also the old viaducts going towards the city.
I think. Someone correct me if I'm wrong?

Indeed. Tower Gateway to Poplar uses the formation of the Blackwall Railway,
which started as a rope-worked passenger line, but after 1926 the route from
Limehouse was freight only, for the docks. Bow Church to All Saints uses the
formation of the North London Railway's docks access, though his section had
passenger trains until WW2. Originally the DLR between Mudchute and Island
Gardens used a viaduct of the Millwall Extension Railway, which was very
much a docks line (parts of it were owned by two of the docks companies,
though the viaduct belonged to the Blackwall Railway). When the DLR was
extended to Lewisham the viaduct was again abandoned in favour of a new
tunnelled route. There are other bits of the DLR which use formations
originally provided for docks lines.

Peter