When TAG talk about saving money the main saving I believe will be in support staff, eg. personnel and various managers which seem to multiply in any Civil Service organisation. TAG have also said that they will buy "off the shelf" systems instead of doing their own R&D. This will see the elimination of R&D costs as well as the loss of the R&D staff. TAG have made a commitment for NATS to be an Air Traffic Control provider and nothing more. This is why over half of the staff will be operational controllers in the future and not admin.
Lets have a bit of faith in the plans TAG have outlined as they do have alot of experience running private aviation companies and British Airways went through the same public to private process within the last twenty years and they seem to be doing okay.