It's a fairly easy job for most builders but be aware it does require planning control as installing the gallow brackets is a structrl modification.
Horrific as it sound I have seen chimney breasts removed with no brackets.
Two breasts? You can take them out up to the loft and put in a steel beam in the loft to support the stacks above. At least that's what a smart person I work with told me. He had two breasts done that way for 2k 5 years ago. Seems good value
Any personal recommendations for people to remove chimney breasts / stacks in east London?