What you need is your new wall to be totally disconnected from the existing wall.
An easy to make cross section would be: Original single brick 50mm air gap Timber stud work with rockwool infill Double skin of plasterboard.
The different masses (RW & PB) are a good combination attenuator, but the key is there must be no hard path for the direct transmission of the sound wave. The studwork should only be connected to the side walls, floor and ceiling, and kept clear of the rear wall.
Toby.