This will come as a surprise to the Privy Council, which has statutory powers enabling the Judicial Committee to consider any matter referred to it by the Queen in Council. In recent times Privy Council inquiries have been held into the legal basis of phone-tapping and events leading up to the Falklands war.
The Judicial Committee was created by Section 4 of the Judicial Committee Act of 1833. Section 21 of the same Act expressly preserves intact the Privy Council's other powers, including what is known as the Royal Prerogative. Thus the right of a subject with a grievance to seek redress by petitioning the Queen in Council has never been abolished.
The "Queen in Council" effectively means the government of the day. The Tories may not want an inquiry into the cash-for-children's-lungs issue, but what about an incoming Labour government?