CIT switched to a traditional JCT contract for More London after using Mace as construction manager for the GLA project.
HBG will construct the £15m ºÃÉ«ÏÈÉúTV 6 that will surround the Greater London Authority's headquarters.
Work will start this month on the seven-storey office and retail block, which was designed by Foster and Partners.
The project team includes QS EC Harris, structural and services engineer Arup and services cost consultant Mott Green Wall.