Property company Grosvenor plans to redevelop Newson’s Timber Yard, which is owned by builders’ merchant Travis Perkins, after it received planning consent in October 2016.
Antiques dealer Humphrey Carrasco and interior design firm Coote Bernardi are among those galleries affected by the proposals.
Travis Perkins applied for the judicial review on March 27. The judge will now begin the process of reviewing the lawfulness of the planning decision made by Westminster council’s planning committee, led by chair Cllr Robert Davis, in 2016.
The planning department is now the responsibility of a new council leader, Cllr Nickie Aiken.
Travis Perkins has argued the decision did not take into account the views of local residents and businesses.
Grosvenor’s plans include the creation of two larger and two smaller shops from the existing five galleries and shops as well as the reconfiguration of five existing flats into seven rental apartments.
Grosvenor said it has offered alternative premises to the businesses affected either in Pimlico Road or nearby.
Newson’s Timber Yard opened in 1845 and Travis Perkins has run it since 1998.