Please consider 3 Ideas; A/B Testing, ROI Based Decisions and Rolling Budgets
A/B Testing
Whatever recommendations the independent review makes I am sure they come with an idea of what will be improved. I suggest progressively rolling out a recommendation (and alternatives) and measuring the effect. If the desired improvement is measured then continue, however if an alternative (or no action) is proving more effective then follow that path.
Return on Investment (ROI) based decision making
I think that the majority, if not all, of the public service provides a greater public benefit than its cost. I suggest that the public benefits be estimated. For example, the Acil Allen Consulting, Report to Defence Science and Technology Group, Economic Impact Case Studies, concluded that there is a 4 to 5 times value generation over the total sum costs. It is wise to allocate public funds to areas with high public benefit and to manage the public service in a way such that the high ROIs are not jeopardized. (Note that every dollar cut from a department with an ROI of x means the public loses x-1 dollars!)
Rolling Budgets
I suspect that there is an end of financial year rush to spend leading to less efficient purchases than a steady-as-you-go spend. Anonymised, metrics could be collected to confirm or deny this suspicion. If it is an issue, granting, public service departments, rolling budgets would solve it.