Just going to provide some clarification here.
The death penalty is forbidden by several pieces of domestic legislation, Art. 3 EHCR, Art. 1 (2nd optional protocol) ICCPR and Art. 6 ICCPR.
The domestic legislation is, in theory, easy to repeal. Regarding Art. 3 ECHR, the only way not to be bound would be to repeal the Human Rights Act, and remove ourselves from the ECHR entirely. However, there would likely be a severe unintended consequence of this. By leaving the ECHR and reintroducing the death penalty, the UK would be in contravention to Art. 3 of the Statute of the Council of Europe, wherein all states commit to guarantee fundamental human rights. This would mean that, per Art. 8 of the Statute of the Council of Europe, the UK may be removed from the Council of Europe entirely. This would be the biggest dressing down that the UK has received since Suez, and would probably mark the end of the UK as a nation that others wanted to associate with in any way whatsoever.
As stated previously, we are also a party to the 2nd optional protocol to the ICCPR, Art. 1 of which (no reservation made by the UK) places a moratorium on the death penalty. Art. 6 ICCPR also serves to accomplish this. While the UK has not signed up to the optional protocol containing an enforcement mechanism for the ICCPR, the UK would be in breach of its international obligations. Per Art. 19 of the Vienna Convention of the Law of Treaties, the UK is not able to make a late reservation under the ICCPR, and as a result would need to exit the ICCPR and attempt to re-enter. This would probably be met with objections from other states.
In short, we have to really, really want to fuck ourselves on the international stage if we're to reintroduce the death penalty.