The government should launch an investigation into Sir Philip Green’s conduct as a company director if allegations emerge that he failed in his obligations while owning BHS, Sir Vince Cable, the former business secretary, has said.

BHS shareholders led by Green, and the billionaire’s family, withdrew more than £580m in dividends, rental payments and interest on loans from the failed department store chain before he sold it for £1 in March 2015. It collapsed into administration this week in a move that crystallised a £571m pensions deficit and has put 11,000 jobs at risk across the UK.

How Philip Green's family made millions as value of BHS plummeted Read more

“The question is whether the dividend payments were disproportionate,” Cable told the Guardian. “It is a question of whether the return on shareholder capital that he was extracting from the company was unreasonable. Was it based on a cynical expectation the company would be forced into administration or was he just over-optimistic about BHS? If there is an allegation of Green’s failure to observe his obligations as a director then it is a matter for investigation by the Insolvency Service.”

The Insolvency Service is a branch of government with the power to strike off company directors for up to 15 years and to mount criminal prosecutions. It is currently awaiting a report from BHS’s administrators before deciding its next steps.

The former cabinet minister’s comments will increase pressure on Green, who is already facing calls to give up his knighthood which he was awarded under Tony Blair’s government in 2006 for services to the retail industry.

Labour MP John Mann has called on him to pay back £400m in dividends to help fill BHS’s pensions black hole or lose the gong. Green has reportedly offered to pay £40m as well as a £40m loan. The government’s Pensions Protection Fund, which is taking on the liability, is expected to pursue him for more than that.

Green could not be reached for comment.

Cable backed the plan of Frank Field MP, chairman of the Commons work and pensions committee, to call Green before MPs to explain the BHS transactions. Cable said if questions remained there should be an investigation.

It would mark a sharp decline in relations between Green and successive governments. In 2010, Green was appointed by the Conservative cabinet office minister Francis Maude to review government efficiency. Maude hailed his “immense commercial experience and of course his fantastic track record at managing large organisations”.

Green’s knighthood was signed off by Tony Blair in the 2006 Queen’s birthday honours, eight months after he banked £1.2bn, the biggest pay cheque in British corporate history. The huge dividend – more than four times the group’s pre-tax profits – came from his Arcadia fashion business, which spans high street names including Top Shop and Burton. It was paid to his wife, Tina, the direct owner of Arcadia who lives in the tax haven of Monaco.

Six months before his honour, Green angered unions by announcing that employees in the final-salary scheme at Arcadia would have to work five years longer to get their pensions, would not receive the same level of inflation-proofing and would have to hike their contributions to maintain benefits. The pensions deficit was a relatively small £11.6m.

He was also attacked by Labour Behind The Label, a pressure group calling for greater rights for textile workers. It criticised Arcadia’s decision not to be a member of the Ethical Trading Initiative.

“Arcadia group is way behind its major high street competitors when it comes to addressing the problems faced by workers making its products,” the group said. “Philip Green has the power to have a real impact on the conditions in which our clothes are produced.”

The questions over Green’s conduct came as the current owner of BHS, Dominic Chappell, said he was working with private US investors to put together a rescue package that would save a “substantial majority” of the chain’s 164 shops and continue the business under the BHS brand.

“The pension deficit was weighing us down and not allowing us to move forward,” he said. “After the administration, when the pensions side of the business is sorted out, we will be able to move on. I’m working with US investors to buy a substantial majority of stores.”

Adminstrators appointed to run BHS are expected to report to the Insolvency Service on why the high street giant collapsed. They have the power to examine current directors’ conduct, and that of previous directors, such as Green, who have been in office in the previous three years.

If there are serious concerns that can be dealt with under civil law then the Insolvency Service can take action, including disqualify directors for anything up to 15 years.

If it is a criminal matter, for example suspected fraud, it could refer it to the SFO or request permission from Sajid Javid, the business secretary, to investigate further and mount its own prosecution.