But the prime minister's official spokeswoman refused to say how much Mrs May was told or even to confirm that there was indeed a fault with the missile.
The missile test in question actually took place when David Cameron was still the prime minister but it has now been confirmed that Mrs May was briefed on the test when she took office.
How much she was told about the test has not been revealed.
"We don't go into operational details beyond that" she said, adding: "The effectiveness of the Trident system is unquestionable."
Asked why this test was not publicised when previous, successful, tests have been the spokeswoman said the release of details was decided on a case by case basis.
She said: "You shouldn't read anything into the fact this one was not publicised."
At no point in this morning's briefing did the prime minister's spokeswoman deny that a Trident missile had failed during the June test.