Davey said that he had "not ruled out moving to" a simpler regulatory system, but said that the Government first planned to work with the profession to reform the existing system "without such significant change".
In a statement to Parliament he said that the responses to the consultation had persuaded him that "a great deal more could be done to improve the effectiveness of, and confidence in, the insolvency regulatory regime".
"My vision is to have a regulatory regime that is transparent, consistent, accessible, independent and accountable," he said.
The consultation followed recommendations made in June last year by the Office of Fair Trading, to address what it perceived as the "weak position" of unsecured creditors under the existing system. It invited views on whether the creation of an independent complaints body would improve confidence in the way complaints and appeals are handled, and whether this body should have the power to review fees.
However, responses to the consultation showed that many insolvency practitioners were "generally not persuaded that fundamental changes to the present regime" were justified.
Alastair Lomax, an expert in insolvency law with Pinsent Masons, the law firm behind Out-Law.com, said that the Government appeared to be listening to the profession and avoiding implementing "change for change's sake".
"This moderate approach should provide greater certainty and clarity. If the objective is a unified, transparent and effective regulatory regime then this is a step in the right direction and good news for the insolvency profession and its reputation in the wider community," he said.
Insolvency practitioners are currently licensed and supervised by eight different recognised professional bodies (RPBs) overseen by the Secretary of State, who also acts as direct regulator of a small number of practitioners.
In his statement Davey announced that the Insolvency Service, part of the Department for Business, Innovation and Skills (BIS), would bring forward proposals to remove the Secretary of State from the process of authorising insolvency practitioners. He also set out plans to cut back the role of the Insolvency Practices Council (IPC), a public body which influences professional standards in the industry.
"The Government is grateful for the useful contributions made by the IPC, but agrees with responses to the consultation which indicate there is no longer a need for an additional body of this sort and its functions would be better placed elsewhere within the regulatory and policy structure," he said.
Frances Coulson, president of insolvency trade body R3, agreed that the insolvency regime in the UK was not in need of radical reform, but added that the profession would work with Davey to consider the possibility of an independent single regulator.
"Insolvency practitioners inherit a challenging set of circumstances with every job, often restricted by limited time and assets, and the threat of redundancies from the failure of the business," she said.
"We recognise the frustrations of unsecured creditors at not receiving the returns they expect and look to greater engagement in the insolvency process. We share the Minister's aim to ensure the regulatory regime is transparent, consistent, accessible, independent and accountable."