His comments come after Downing Street revealed Theresa May had been briefed about a Trident test following reports an unarmed missile went off course.
The incident, which apparently saw the missile head towards Florida instead of the west coast of Africa, took place shortly before a Commons vote on whether to renew the defence system or not - something MPs did.
The vote saw MPs vote overwhelmingly in favour of spending up to £40 billion to renovate Trident.
The Prime Minister's official spokeswoman declined to confirm or deny reports that a missile malfunctioned during the test, stating only that Mrs May was told the operation was completed successfully.
During a TV interview on Sunday with Andrew Marr, the Prime Minister ducked questions about the incident four times.
Rev David McLachlan, from Scottish Christians Against Nuclear Arms, told Premier News Hour he believes the government purposely hid the failure.
Rev McLachlan: "Well it's obviously a cover up. It's very interesting the Prime Minister refused to answer the question.
"If Theresa May did know, then why didn't she tell people before the Commons had a vote on renewing Trident? That was obviously held back deliberately."
He added that the public and MPs had a right to know all the information about the failed nuclear test before a decision on the future of Trident was made.
"If we're going to ask our MPs to make decisions, they should have the full facts in front of them. If something like this is happening then then the public really need to know because this is a huge amount of money that we spend on these things and there's a huge debate to their morality and their usefulness."
A government spokesperson told Premier that Trident was key to UK security.
They said: "The capability and effectiveness of the Trident missile, should we ever need to employ it, is unquestionable... We have absolute confidence in our independent nuclear deterrent."
Listen to Premier's Alex Williams speaking to Rev David McLachlan on the News Hour: