The figure owed by Dame Shirley includes interest and a breach of trust charge on the initial amount of £26.5m, but she claims her assets are only worth a few hundred thousand.
But research by Radio Four?s Today programme appears to show she still has influence over the family?s millions via a number of off-shore companies.
The council has spent £500,000 in the past 18 months in attempts to force Dame Shirley to pay up.
The Audit Commission appealed for help tracking down Dame Shirley?s assets.
The surcharge was imposed after Dame Shirley tried to gain political support by selling off council homes to potential Conservative voters when she was council leader.