The firm won the job worth up to £5om back in November. Contractor Keltbray has started the demolition contract for the building know as W4 at 169-183 Regent Street.
Steelwork to support the building facade has been put in place to allow demolition of the existing building structure which got underway last month.
Buildings are also being cleared within New Burlington Mews.
Mace will build 50,000 sq ft of retail space at ground level with 140,000 sq ft of office above
The project is part of the £1bn Regent Street Vision investment by Crown estates in the famous shopping street.