Little said that English had known about the recording 18 months ago but had never acknowledged this in media interviews and had stood aside while Barclay denied its existence. That was a " total failure of leadership," he said.
New Zealand First leader Winston Peters went further, saying that English and former Prime Minister John Key had been complicit in hiding illegal activity.
"When you aid and abet a crime, and when you are involved in hush money and a cover-up, then there are serious questions to be answered."
Police closed the investigation last year without pressing any charges. A spokesman said this morning that they were assessing the information which had come to light in the last few days "in relation to any impact on the findings of the original Todd Barclay inquiry".
Barclay refused to be interviewed by police during the investigation last year, after taking legal advice. While English told police about the recording, he did not know whether Barclay was in the room when it was made - a crucial factor in whether Barclay committed an illegal act.
Little said there was now "ample" information for the police to reopen their inquiry. It was his understanding that police did not progress with an investigation last year because of doubts about whether a recording was intentional. English's statement to police appeared to indicate intent, he said.
"There is enough there to draw an inference that there was a level of deliberateness in the recording of conversations that Glenys Dickson was party to."
Peters also believed police should reopen the case.
He compared the police's reaction to the "teapot tapes" scandal, when a cameraman was accused of illegally recording a conversation between former Prime Minister John Key and former Act leader John Banks.
"You know what happened in the Bradley Ambrose case, the trouble they went to. They were beating down the doors of the media to get to the truth.
"So look at the difference in drive, unction and ambition in that matter."
MPs also raised concerns about an allegation in a Newsroom story that a National Party board member put pressure on Dickson to drop her complaint to the police.
The Herald has since revealed that the board member was Glenda Hughes, a PR consultant and former police officer.
Green Party leader James Shaw said the police needed to investigate the allegation - a possible obstruction of justice.
Barclay's National colleagues expressed sadness about his imminent departure today.
Deputy Prime Minister Paula Bennett said it was "a really sad day" and that Barclay had "a big career ahead of him" before his decision to quit.
Barclay had been going through "a really hard time reflecting on what his next moves were", she said.
Revenue Minister Judith Collins, one of Barclay's supporters, also said it was a "sad day".
She had advised Barclay over the last few days, but would not say whether she told him to resign.
"Todd's phoned me a couple of times, and I've just given him the support I would give any colleague who is going through tough times.
"I'm very aware he is a very, very young man to be in a place like this and it's just really tough, politics."
