Pray remember The European Court of Justice. If the terr huggers don't get a result in the Lords they still have the ECJ. As the Septics still have the death sentence, that may just be Capt Hook's get out card; as I understand it.
An appeal in the ECJ would only be referred or heard there if the case was in relation to a provision of European Law (e.g. Human Rights Act); as this case is in reference to the The 2003 Extradition Act, a UK law, then the UK judicial appeal process is the final one.
As stated previously, the House of Lords is the final court of appeal in England, Wales and North Ireland in both civil and criminal matters (and for Scottish civil matters).
The appeals are referred to and heard by Lords or Appeal in Ordinary, generally known as the Law Lords, of which there are currently twelve. 'In Ordinary' means that the Lords work full time on the judicial business of the House of Lords and receive a salary. Their salary is paid from a consolidated fund (revenues hld in the Exchequer account at the Bank of England), which helps ensure their independence.
A person wishing to appeal to the House of Lords must seek leave to appeal by petition. Petitions are considered by an Appeal Committee of three Law Lords. The Committee's decision to allow or refuse a petition will depend on whether the case involves a point o law of general public importance that ought to be considered by the House. The Appeal Committee works mainly on the basis of written submisions. Each year about hree hundred and fifty applications are made for leave to appeal and about a hundred are allowed.