David Calvert-Smith says that in cases such as murder, rape or serious assault a suspect should be retried if there is compelling new evidence, such as DNA profiling, or a confession.
He adds that although in general, he supports the double jeopardy rule, it was "a scandal" that criminals could brag about their crimes without fear of legal reprisal.
The Law Commission recently recommended that the double jeopardy rule be altered in the light of the Stephen Lawrence murder case which saw three of the five suspects cleared of the teenager's murder.
Calvert-Smith stresses however, that police incompetence should not be the only reason to allow a retrial: the prosecution, he says, should be allowed a second go only when a defendant has been tried, acquitted and fresh evidence has emerged.
He predicted that the Law Commission's proposals, if implemented, would only lead to a "handful" of retrials each year