No, Britain should not use Capital Punishment as Capital Punishment is a gross violation of the right to life. Even if an offender has committed a heinous crime, that individual still has a right to life, and to violate that right to life would make a government just as heinous as that offender.
I agree with Iain Hislop on this where he says that we would end up convicting people who are later proven to be innocent. Moreover, it is simply the easy way out of the problem and would not deal with reformation. Also, it has not proven to be a deterrent in America so why should it prove effective in Britain? Shootings commonly occur when someone is not thinking straight and there is little chance for them to reflect on the morality of the decision.