To extradite without such a guarantee is a blatant violation of the UK's obligations as a signatory of the ECHR, as to do so would violate his right to life.
If there's any reason to suspect that no such guarantee exists, they may well apply to the ECtHR after any Supreme Court decision to extradite him, and it would be unlikely that he'd be extradited until the ECtHR judgment had happened.
That said, if it comes to light after he's been extradited any application to the ECtHR would likely do little for him, though it would be politically damaging.
>'The BBC's security correspondent Frank Gardner said a senior British government official told him that this case was not the first time that the UK had dropped its request for assurances that the death penalty would not be used.'
>'What ministers and MPs believe is that Mr Javid is attempting to smooth the way for the Americans to take the cases by letting them know that the UK will not, for once, kick up a fuss about the death penalty.'
>'In other words, this is all part of a deal. And some sources suggest this is a deal with precedent, that this is not the first time the UK has turned a blind eye towards its death penalty policy.'
>'The Security Minister, Ben Wallace, told MPs that it had happened before but not while he has been in his job.'
>'He explained that little-known guidance to ministers, known as the Overseas Security and Justice Assistance guidance, that was last updated January 2017, allowed the Home Secretary to make an exception to the rule.'
>'It states "written assurances should be sought before agreeing to the provision of assistance that anyone found guilty would not face the death penalty" but "where no assurances are forthcoming or where there are strong reasons not to seek assurances, the case should automatically be deemed 'High Risk' and FCO Ministers should be consulted to determine whether, given the specific circumstances of the case, we should nevertheless provide assistance".'
There is reason to strongly suspect that no such concrete guarantee exists and it is in fact entirely down to the personal whims of whomever currently happens to occupy the Home Office, while the Foreign Office is busy keeping an image going of something entirely different. As is tradition.
If there's any reason to suspect that no such guarantee exists, they may well apply to the ECtHR after any Supreme Court decision to extradite him, and it would be unlikely that he'd be extradited until the ECtHR judgment had happened.
That said, if it comes to light after he's been extradited any application to the ECtHR would likely do little for him, though it would be politically damaging.