The final abolition in 1998 came about as a result of the UK�s Human Rights Act of that year. Under the European Convention on Human Rights (ECHR) - which the 1998 Act incorporated into domestic law- the death penalty was not permitted. A number of signatory states to the convention still had the penalty available but did not use it. This was because those sentenced to death could take their case to the European Court of Justice and would almost certainly succeed.
The 1998 Act formally incorporated those provisions into UK law. As it stands now, even if all the electorate, including all the MPs and Lords, wanted to restore capital punishment we would be prevented from doing so by both the 1998 UK Act and the ECHR. To enable such a restoration we would have to repeal the 1998 Act and withdraw from the ECHR.
Both of these courses of action are unlikely in the extreme. Indeed withdrawal from the ECHR would almost certainly jeopardise our membership of the EU. So this one issue demonstrates quite adequately that the UK Parliament cannot decide matters of importance for the UK electorate.