Mr Campbell was speaking yesterday during a debate in Westminster Hall at the House of Commons centred on a world-wide ban on capital punishment.
He said there were circumstances when the death penalty were appropriate. He contended that the penalty could be implemented within a robust legal framework.
The DUP MP said the death penalty could only be used as a punishment for the most serious crimes carried out by serial offenders.
However, he said there was little chance the death penalty would be reintroduced in the UK because of a "cosy consensus" amongst politicians although he said opinion polls show the majority of people agree with him.
He said later: "There are times when the death penalty, operated within a robust legal framework, is an appropriate form of punishment. We can all think of mass murderers who through their evil acts forfeited their right to life.
"I have no compunction at all in saying that someone like Ian Brady, the Moors Murderer who murdered five innocent children has forfeited their right to live through their actions. The argument that lifetime detention would prevent a repeat killing does not apply if a killer escapes from detention, it would not be the first time that an escape carried out by killers have occurred.
During the debate at Westminster Hall, I expressed what I believe to be the majority opinion in this country that the death penalty should be retained for use in certain circumstances."