If I remember correctly, there was once a time when convicts on whole life tariffs were never told they had no possibility of parole. But that later changed.
I believe it is wrong for home secretaries to interfere with the judicial process.
The home secretary has the power to pardon convicts. The CCRC can also recommend pardons to the home secretary. This is in circumstances where the system has epically failed, i.e a convict is factually innocent, all avenues of appeals are exhausted and thus exculpatory evidence is inadmissible on technical grounds.
Such mechanism should exist. But I doubt it will ever be carried out on a conviction where the convicted is still alive.