Lord George Robertson, a former Labour defence secretary, will use a speech to accuse "non-military experts in the Treasury" of "vandalism".
Chris Walker says he will name staff from five agencies unless suitable disciplinary action is taken.
The families of Nuria Sajjad and Selena Lau, who died at an end-of-term tea party, say the initial investigation was flawed.
There are questions over whether local taxpayers are picking up any of the bill for policing the visit.
The BBC spoke to people in Sydney to hear their thoughts on the Duke and Duchess of Sussex’s trip to Australia.