The move follows a deal struck between Dame Shirley (Con) and the council for a final settlement of£12.3m for her role in the 1980s homes for votes scandal. She owes over£40m.
Westminster said most of the money would be devoted to social housing.
Wrekin MP Peter Bradley, a former Westminster Labour councillor, called on the Metropolitan Police to probe Dame Shirley for perjury over her earlier claim to have assets of only£300,000.
Mr Bradley said he would write to Audit Commission chairman James Strachan 'to ask whether he has endorsed this shabby deal'.
Commission chief executive Steve Bundred said the quango had been 'consulted by Westminster at every stage of this process,' though he did not expressly endorse the deal.
Dame Shirley was surcharged£27m by district auditor John Magill after a protracted series of legal battles.
Deputy leader Kit Malthouse (Con) said he expected social housing to take 'a majority' of the money after costs were met.
The deal represented 'absolutely the best we could expect', and had recovered more money than anyone except 'Labour obsessives' thought possible.
'This has gone on for almost 20 years. It has blighted Shirley's life. I think it has even blighted people like Bradley,' Mr Malthouse added.
To succeed, a perjury action must establish that a person knowingly made an untruthful statement under oath.
David Corker, a solicitor with experience of such cases, said: 'My guess is she will have found the£12m from money covered by trustees, from which she therefore has a nominal distance and legally that would give her a defence.'