The Sun said the first-stage boosters on the missile, which was equipped with dummy warheads, did not ignite.
The report included a statement from the Ministry of Defense (MoD) acknowledging an anomaly had occurred during the test.
"As a matter of national security, we cannot provide further information on this, however we are confident that the anomaly was event specific, and therefore there are no implications for the reliability of the wider Trident missile systems and stockpile," the MoD statement said, Reuters reported.
"The UK's nuclear deterrent remains safe, secure and effective."
The MoD could not immediately be reached by Reuters for comment.