The contractor, which has offices in the capital, was awarded a pre-construction services agreement by developer Great Portland Estates for St Lawrence House in Soho.
The building will feature six levels of high-quality office space as well as ground and lower-floor retail.
It is aiming for an Excellent rating through environmental initiative BREEAM, and will feature photovoltaic cells and natural ventilation.
The project started on site in April, with existing buildings being demolished, and is due for completion in February 2016.
BAM is in discussions with the client over the main construction contract for the build.
BAM project manager Rob Biddle said:
“This is a high profile job in the centre of London’s historic Soho district.
“We are using all our skills and experience to ensure the project is a success for the eventual end users as well as the local population and environment.”
BAM is known for numerous signature projects in London, undertaking many of the current office projects at Argent’s the developments of Kings Cross, and recently completing headquarters for the likes of Macmillan, Burberry, Unison and Cancer Research UK.