Collating two reports, the Times and CNN, this would seem to indicate the missile itself was performing nominally, it was a failure in the range safety abort system which triggered the self-destruct mechanism.
Times: "The £17 million unarmed D5 missile is believed to have been obliterated in an automatic self-destruct sequence when it went off course after being launched from HMS Vengeance off the coast of Florida. A failure in the data communications system of the US-made weapon system has been blamed."......
CNN: "Britain's Sunday Times newspaper reported that the missile veered towards the US coast, but the US official told CNN that this trajectory was part of an automatic self-destruct sequence. The official said the missile diverted into the ocean -- an automatic procedure when missile electronics detect an anomaly."