"...that there are certain Law Lords who still have a very big influence:"
But as I said, there are no "Law Lords", Zacs. Lord Justice Treacy and his predecessor Lord Justice Leveson, who are mentioned in the information on the Sentencing Council, are Justices in the Supreme Court and play no part in the business of the House of Lords. The current Lord Chancellor (also mentioned) is Chris Grayling, MP, a member of the House of Commons. The "Lord" in their titles is no more reference to the House of Lords than is a High Court Judge when referred to in court as "My Lord".
The whole idea of the Constitutional Reform Act of 2005 was to fully separate the judiciary from the executive. Hence the setting up of the Supreme Court and the removal of judicial functions from the House of Lords.
Whilst I do not fully accept that the sentencing council is truly independent (there is far too much "government consultation" involved in their brief and the secretary of State has a place on their "board") it is not true to say that the Sentencing guidelines are overseen by the "Law Lords".