presenter skewered minister Alison McGovern with a barrage of questions over the Southport murders.
The Government has come under fire for withholding information from the public about the incident being treated as terrorism.
On Monday , 18, pleaded guilty at Liverpool Crown Court to murdering three young girls in a knife attack at a Taylor Swift-themed dance class in .
He was referred three times to the Government's counter-terrorism programme, Prevent One, following concerns about his potential interest in the killing of children in a school massacre.
Appearing on Sky News on Wednesday, the employment minister and Birkenhead MP said: "I just know that wouldn't want to do anything that could put a prosecution at risk."
But Burley interrupted her to ask: "How would it have put a trial at risk?
"I don't get it, because in October of course, it was announced he was charged with the ricin in his house and also the terror manual that he had downloaded. So the details were revealed before the trial, so obviously it couldn't prejudice a trial."
Ms McGovern said "politicians' words can have consequences" but Burley replied: "Why withhold information from the public when it's so important?"
Ms McGovern was forced to say that questions would be answered in the inquiry, stuttering slightly as she said: "I understand people's concern. The most important thing is we were able to get some tiny bit of justice for those families."
Burley insisted: "That's nothing to do with Keir Starmer not telling us that this could well have been a terror incident. It didn't stop him in 2017, for example, when he tweeted about the Finsbury Park bombing and saying then that it was a terror attack."
Ms McGovern apologised and again stuttered as she pleaded with the host to understand the situation.
Burley replied: "You understand the Prime Minister should be telling us what's going on? It's a privilege that he has that job. He should be telling the people of the country what's happening. That's nothing to do with the court case, is it?"
