Now that the company has been made insolvent, the administrators Duff & Phelps will be able to track and retrieve BHS assets for the company and its creditors.
The judgement took place on 5 May and was expected to be released days later, but it was only formally handed in on Tuesday morning.
The application for permission to appeal was made orally to Registrar Briggs on Tuesday, which he subsequently refused.
RAL now has the opportunity to renew its application for permission to appeal to a single judge of the High Court within 21 days.
Retail Acquisitions bought BHS from its former owner, the retail magnate Sir Philip Green, for £1 in March 2015. It then fell into administration in April 2016, with a £571m pensions deficit.
Lance Ashworth, insolvency specialist at Serle Court Chambers, said, “The registrar’s judgment shows RAL to be heavily insolvent, despite having received substantial sums from BHS.”
The judgement found RAL to have an “endemic” shortage of working capital, and the value of its assets to have been substantially overstated.
Ashworth added, “The appointment of a liquidator will result in a closer scrutiny of RAL’s current, and previous, asset position and dealings. No doubt the liquidator will seek to establish precisely what occurred within RAL following its acquisition of BHS, and what became of the monies RAL received from BHS.
“In the event the liquidator finds monies to have been paid out improperly he has powers to recover them – in particular from related persons such as Mr Chappell.”
A Duff & Phelps spokesperson said in a statement, "Duff & Phelps, acting on behalf of BHS Group, is satisfied that RAL has been put into liquidation.
“The process of realising the assets of RAL can now commence to the benefit of all the creditors of the BHS companies."
In February this year, The Pensions Regulator (TPR) agreed a cash settlement worth up to £363m with Sir Philip Green to help plug the gap in the BHS pension scheme, ending months of uncertainty for thousands of former workers and members of the scheme.
Green agreed to provide funding for a new independent pension scheme offering former staff the same starting pension as they were originally promised by BHS.
Chappell told a panel of MPs in June last year that BHS could have been saved if Sir Philip Green had assisted Chappell and RAL instead of calling in the administrators.
He added that RAL's mistake was not raising more money to protect the business. He also admitted that RAL was part of the downfall of BHS and apologised for the “avoidable” loss of 11,000 jobs.
In a damning report on the downfall of the high street chain, MPs concluded that Sir Philip Green was ultimately to blame for the collapse of BHS after rushing to offload the troubled retailer, which was losing money and burdened with a massive pension fund deficit to the “manifestly unsuitable” Dominic Chappell. The report also highlighted the failings of the advisers involved in the transaction.