The hedge fund's case comes after the near-collapse of the lender in the credit crunch last year - which necessitated its eventual nationalisation in February.
SRM and other shareholders claim that the terms of this government deal are disadvantageous, alleging that the takeover effectively amounted to public "misappropriation" of privately-owned assets.
It is understood that the shareholders are to use existing European Union human rights legislation and national case law in its bid to claim better terms, the Times reports.
The interested parties' application for judicial review terms the government's financial offer as "factually and intellectually dishonest".
An (anonymous) shareholder added: "You don't go into litigation lightly and you don't sue the government lightly."
The UK government has yet to respond to the legal threat.