Sir Philip Green is facing an uphill battle in his attempt to bail out BHS’s pension fund after the British vote to leave the European Union added about £100m to the potential bill.

As MPs prepare to publish a report on the demise of BHS on Monday, Green is in talks with regulators and pension fund trustees about how to fulfil his promise to “sort” the failed department store’s pension deficit, which stood at £571m on one measure at the time of the company’s collapse.

Industry experts said a plunge in the value of gilt yields after the EU referendum had contributed to a near 19% rise in the average value of pension deficits controlled by the Pension Protection Fund (PPF), a lifeboat scheme funded by levies on industry, between February and June. This indicates a rise of about £100m for the BHS scheme.

In order to ensure members of BHS’s schemes receive full pension benefits, Green’s total bill could now be about £670m, valued on a buyout basis that includes the assumed overheads that an insurance company would seek to recoup.

Green, who sold BHS for £1 to the formerly bankrupt Dominic Chappell about a year before the retailer went into administration, remains responsible for bailing out the pension deficit as regulators have powers to pursue former owners.

The former BHS owner is thought to be hoping to work out a deal under which he could use cash lump sums to buy out members of the pension scheme who have savings of less than £18,000. That would leave a small number of remaining members who could transfer to a new scheme, potentially knocking hundreds of millions of pounds off Green’s bill.

A spokesman for Green’s Arcadia Group declined to comment but sources close to the company admitted the deal would need more work given Brexit’s impact on the pension deficit.

Lord Myners, the former M&S chairman who is working as an adviser to MPs investigating BHS’s pension problems, has suggested such a deal could cost about £400m.

Green began working on the plan, then named Project Thor, when he owned BHS, but decided to sell the business before a deal had been agreed. When BHS went into administration, the pension scheme automatically fell under the auspices of the PPF.

Pensions experts said the PPF’s rules meant it would now be much tougher for Green to buy out BHS fund members with small pension pots. The lifeboat’s rules do not allow him to buy out individual members unless its lawyers can be assured that no members of the scheme are disproportionately benefiting or losing out.

John Ralfe, an independent pensions expert, said no such deal had ever been agreed with the PPF and it would be difficult for Green to break new ground.

An alternative would be to move all members to a new scheme and then offer to buy out those with small pension pots – potentially a highly expensive move.

“There is no clever ‘financial engineering’ solution available. The only way for Sir Philip to square the circle, and remove the threat of legal action, is to agree a big cash payment with the Pensions Regulator,” Ralfe said.

Frank Field MP, chairman of parliament’s work and pensions committee which has been investigating the demise of BHS, said: “Sir Philip can break the logjam by signing a cheque. The only restraint is his generosity.”

Given the complexity of agreeing a deal within Green’s budget, it’s thought to be unlikely that pensioners will hear about the future of their savings before the end of the year.

Chris Martin, chairman of the BHS pension fund trustees, said: “The trustees are really positive about the possibility of finding a solution but are also very conscious that sorting out the practicalities and technical complexities may take some time.”

The importance of the PPF reaching a deal with Green was laid bare on Thursday. The body’s annual report revealed that the value of claims on the PPF rose by £322m to £476m in the year to the end of March, with BHS making up more than half the value of all claims on the pensions lifeboat in the year.

For technical reasons, including its ability to trim benefits to members by 10%, the cost to the lifeboat of bailing out BHS’s pensions scheme is £275m.

On Friday, a second administrator tasked with investigating the role of former directors was appointed to BHS after pressure from the PPF. FRP Advisory will work alongside the existing administrators at Duff & Phelps.