The contractor, which rebuilt the former Belmarsh West prison under a PFI deal last year, aims to build a new house block containing 216 new cells at the Category B prison.
The new four storey L-shaped block together with a new industries building and basketball court will see the demolition of existing works departments for neighboring Belmarsh mens prison.
Under the expansion plan the existing 5.2m precast concrete wall will be extended to enclose the new buildings.
The new house block will essentially be formed from pre-cast concrete components and founded on bored piles.
Under the present plan Skanska hopes to start enabling works, which will include diverting a water main this summer.