The National-led Government would be unable to pass three pieces of legislation including major child, youth and family reforms if MP Todd Barclay had been sacked immediately, the Labour Party says.
Barclay announced last week he would quit politics at the election after a secret recording scandal, and Labour leader Andrew Little said he was only being kept in Parliament to preserve National's majority.
Without his vote, the National Party would need support from two out of three of its coalition partners to pass legislation.
Labour said there were three bills before Parliament which were either opposed by the Maori Party or by both Act and United Future, meaning they would not progress without Barclay's vote.
The bills included National's major reforms of Child, Youth and Family (CYF).
Little said National's majority was resting on an MP who had recorded his staff and refused to co-operate with police.
Barclay declined to be interviewed by police during an investigation last year which stemmed from a complaint by the Clutha-Southland MP's former staffer Glenys Dickson.
Newsroom reported last week that a National board member warned Dickson to withdraw a police complaint against the MP because "if National didn't have Barclay in Parliament they were one short to pass legislation".
The police investigation was closed after 10 months without any action being taken. It was reopened by police yesterday to check whether new evidence had an impact on the original investigation.
English said yesterday it was up to Barclay whether he wanted to remain as an MP while the investigation was taking place.
"There have been a number of investigations into MPs at different times, including quite recently. And the MPs have not stood down," he said.
"That's ultimately Todd's decision."
If charged with making an illegal recording, Barclay would be forced to leave Parliament because it was punishable by up to two years' jail - the threshold at which MPs must resign.
Police could not give a timeframe for their new investigation or say whether it would be completed before the September election.
The three bills highlighted by Labour are set to be passed into law in the next six weeks.
Labour also said six bills which hinged on Barclay's vote had passed since English was alerted to the fact that Barclay recorded a staff member.
They included the legislation required to implement the Trans Pacific Partnership.
Government Bills which are remaining to be passed this term which will depend on Barclay's vote (based on known party position)
• Children, Young Persons, and Their Families (Oranga Tamariki) Legislation Bill
• Local Government Act 2002 Amendment Bill (No 2)
• Employment Relations (Allowing Higher Earners to Contract Out of Personal Grievance Provisions) Amendment Bill
Bills which passed by one vote since the end of February 2016 when the Barclay incident happened
• Housing Legislation Amendment Bill
• Social Security (Extension of Young Persons Services and Remedial Matters) Amendment Bill
• Trade (Anti-dumping and Countervailing Duties) Amendment Bill
• Trans-Pacific Partnership Agreement Amendment Bill
• Employment Relations (Allowing Higher Earners to Contract Out of Personal Grievance Provisions) Amendment Bill (National Party members bill - still before the House)
• Social Security (Stopping Benefit Payments for Offenders who Repeatedly Fail to Comply with Community Sentences) Amendment Bill (National Party members bill - still before the House)
(Source: Parliamentary Library/Labour Party)