Skanska, which is managing the project, gained approval from Wandsworth Council to remove and rebuild the three remaining chimney stacks.
The council has officially signed off the first stage of rebuilding work to the south west chimney of the power station.
The chimney now rises over 25m above the brickwork washtower, more than halfway to its full exposed height of 40m.
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It will be restored to its full height of 50m before the end of 2015.
The Battersea Power Station Development Company (BPSDC) is now permitted to begin rebuilding the other three chimneys, which are expected to be complete in late summer 2016.
The rebuild programme uses the original construction methods to ensure the visual appearance of the new chimneys matches their predecessors as closely as possible.
Skanska is undertaken the programme alongside two other specialists contractors, Beroa Bierrum and Buro Happold Engineering.
Rob Tincknell, Chief Executive Officer at BPSDC, said: "Reaching the halfway point on the first chimney to be rebuilt is another significant milestone for everyone involved in the redevelopment of Battersea Power Station."
(LM/CD)
