Ministers have been accused of covering up the failed test which saw the launch of an unarmed Trident II D5 missile from a British submarine off the coast of Florida in June.
The missile is said to have malfunctioned and was never revealed to MPs.
Labour former defence minister Kevan Jones demanded an inquiry into claims the launch of The said the cause of the failure remained top secret but questions could be asked over the Government's failure to publicise the failed test weeks before MPs approved the £40billion Trident renewal programme in July.
Previous tests have been publicised by the Government.
Prime Minister Theresa May today refused to deny she knew about a failed test of the Trident nuclear deterrent when addressing MPs before a crucial Commons vote on the future of the submarine-launched missile system.
Mrs May repeatedly failed to answer direct questions on her knowledge of the test when appearing on the Andrew Marr show today.
The Prime Minister has refused to explain if she knew about a failed test of the Trident nuclear
I have absolute faith in our Trident missiles
Speaking on the BBC One show Mrs May said: "I have absolute faith in our Trident missiles.
"When I made that speech in the House of Commons, what we were talking about was whether or not we should renew ourTrident, whether or not we should have Trident missiles, an independent nuclear deterrent in the future.
"I think we should defend our country, I think we should play our role in Nato with an independent nuclear deterrent.
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The UK's Vanguard fleet of four submarines carrying Trident nuclear missiles are due to become obsolete by the end of 2020
"Jeremy Corbyn thinks differently, Jeremy Corbyn thinks we shouldn't defend our country."
Asked again, Mrs May replied: "The issue we were talking about in the House of Commons was a very serious issue.
"It was about whether or not we should renew Trident, whether we should look to the future and have a replacement Trident.
Mrs May’s failed to answer direct questions when appearing on the Andrew Marr show today
"That's what we were talking about in the House of Commons, that's what the House of Commons voted for."
When host Andrew Marr asked about her knowledge of the test for a final time, Mrs May said: "There were tests that take place all the time for our, regularly, for our nuclear deterrents.
"What we were talking about in that debate that took place was about the future."
Host Andrew Marr asked about her knowledge of the failed test of the Trident nuclear
But Labour, whose leader Jeremy Corbyn is staunchly against the use of nuclear deterrent, described the “cover-up” as “ham-fisted.
He told the Sunday Times: "The UK's independent nuclear deterrent is a vital cornerstone for the nation's defence.
"If there are problems, they should not have been covered up in this ham-fisted way.
Labour leader Jeremy Corbyn is staunchly against the use of nuclear deterrent
"Ministers should come clean if there are problems and there should be an urgent inquiry into what happened."
A Government spokesman remained equally as tight-lipped as the Prime Minister.
They said: "The capability and effectiveness of the Trident missile, should we ever need to employ it, is unquestionable.
Mrs May today refused to deny she knew about a failed test
"In June the Royal Navy conducted a routine unarmed Trident missile test launch from HMS Vengeance, as part of an operation which is designed to certify the submarine and its crew.
"Vengeance and her crew were successfully tested and certified, allowing Vengeance to return into service. We have absolute confidence in our independent nuclear deterrent.
"We do not provide further details on submarine operations for obvious national security reasons."