The Petition of affidavit to parliament is an application to parliament as an alternative procedure

The civil practice directions 8A lists types of applications to the high court under certain acts.

This gives example and insight into that a petition to parliament is.

An application to parliament (in the form of an affidavit by petition) under the 1688 bill of rights.

To the Jurisdiction of parliament.
Not the high court or Queens Bench.

These, Greivences , petitions, complaints are noted as valid alternative procedures in the House of lord acts.

The law and right to do this still exists.
And petitioning through the public petitions can be passed between departments or submitted to specific committees or offices of Government such as the office of JCIO in the Royal courts of Justice operating under the Lord Chief justice and Lord Chancellor Jurisdiction

procedure