Understood to be worth around £460m, the complex Grade II building conversion is thought to be the biggest single-stage, fixed-price building contract to be let in the country.
The vast Edwardian building, where Winston Churchill once worked and whose 1,100 rooms are linked by more than two miles of corridors, is being redeveloped by the Hinduja Group and Spanish firm OHLD.
Ardmore, which has delivered a string major London hotel conversions and new build projects in recent years, beat rivals Sir Robert McAlpine and Mace who had offered the client a construction management route to deliver the complex project.
Construction specialist Toureen has been on the job carrying out enabling works for around a year and will be novated to Ardmore.
The firm has now raised hoardings around the site where it will create the 125-room five-star hotel and 85 luxury apartments.
The complex project will double the number of floors from seven to 14. This will include adding three extra floors to the top as well as extending the existing two-floor basement down with four extra basement levels.
A new 25m swimming pool and ballroom will be built in the new basement below the existing central quadrangle.
Designs have been drawn up by EPR Architects alongside structural engineer Elliott Wood and services engineer Aecom with Gardiner & Theobald acting as cost consultants.