Sir Philip Green’s family is to pay a promised £50m into their fashion empire’s pension scheme within the next 10 days – almost a year earlier than scheduled – as the business secretary, Alok Sharma, called on the insolvency watchdog to investigate the handling of the failed group.

Sharma has asked the insolvency watchdog to examine whether the conduct of directors at Green’s Arcadia Group, which owns a string of high-street brands including Topshop, Dorothy Perkins and Burton, led to problems for the group’s pension fund.

Arcadia fell into administration on Monday, leaving a pension deficit estimated to be as much as £350m.

Last year, Green’s wife, Tina, who lives in Monaco and is the ultimate owner of Arcadia, pledged to pay an extra £100m into the group’s pension scheme over three years and signed over rights to property worth £210m. The pension scheme also has a claim over a debt owed by Topshop to the main Arcadia Group.

Tina Green has so far paid £50m of the promised extra funding. On Wednesday, Arcadia said she would pay the outstanding amount within the next week to 10 days. The final instalment was not due until September 2021.

Despite the additional cash, there are concerns that the pension scheme’s funding will fall short because the pledged property assets are likely to have fallen in value. The Greens are under pressure to deal with Arcadia’s pension deficit as the group is the second major retailer linked to the family to collapse with a scheme in the red.

The department store BHS went into administration in 2016 with a £571m pension deficit only a year after Green sold it for £1 to Dominic Chappell, a former bankrupt. Green eventually paid £353m to support the BHS scheme after pressure from the Pensions Regulator.

The Arcadia deficit is also controversial, as the Green family benefited from a £1.2bn dividend from the company in 2005, as well as more than £300m in interest payments on loans and rents on properties that the family owned.

Sharma called on the Insolvency Service to take a “rigorous” look at the actions of directors at Arcadia. Within three months of being appointed, administrators must provide the regulator with a report on directors’ behaviour. The agency will then consider whether there are grounds for further investigation.

In a letter to Dean Beale, chief executive of the Insolvency Service, Sharma said: “Given the significance of this case and its implications for thousands of suppliers, pensioners and employees, I would be grateful if you would review this report rigorously.

“If you decide that there are grounds for an investigation, I would ask that it looks not only at the conduct of directors immediately prior to and at insolvency, but also whether any action by directors has caused detriment to creditors or to the pension schemes.”

Boris Johnson highlighted Sharma’s action in parliament, adding: “We will be doing everything we can to restore the high streets of this country.”

Arcadia’s pension fund is being assessed for entry to the Pension Protection Fund, the industry-backed lifeboat that pays pensioners of collapsed companies. Under the scheme, members who have not reached normal retirement age before the date their employer goes into administration could lose 10% of their benefits, even if they have already started taking the pension.