One of my concerns about Brexit is that countries with EU membership must not have the death penalty, it's a condition of being a member. When we leave the EU, the UK could very well reinstate it
--FACT ALERT (idiots might want to look away)
The UKs prohibition on the death penalty has nothing to do with the UKs membership of the EU, but the UKs acceptance of the 1953 European Convention on Human Rights (ECHR).
It is a pre-requisite of EU membership that a member state also be a signatory to the ECHR.
The UK is - as it has always been - free to leave the ECHR at any time. Where it could join Russia as the only country invited to sign that has declined.
The death penalty was suspended in the UK in 1965 (just a month or two before it could have taken Brady and Hindley) and that suspension was made permanent in 1969 (under Labours James Callaghan as Home. Sec) and 1973 in Northern Ireland.
in 1985 protocol no. 6 was signed into the convention making capital punishment unlawful in member states (so including the UK).
Subsequently the ECtHR has ruled that the US implementation of the death penalty contravenes the ECHR which means that anyone extradited from an ECHR signatory cannot be tried for a capital crime. (Canada has a similar approach).
--FACTS END
Whilst successive (Tory) governments have made a lot of noise about withdrawing the UK from the ECHR, it's unlikely in practice since it would mean a lot of ECHR countries could no longer work with UK law enforcement. Hardly the hallmark of a government that gives a shit about law and order. And as recent events in Louisiana demonstrate, "laws" are just what governments say they are. Which is why a backstop like the ECHR is essential in protecting us from the power of the state.
We have yet to see it play out, but the ECHR is going to play a central part in the Assange extradition case, depending what charges - and potential penalty - the US government are putting on the docket.