The police watchdog is "woefully under-equipped and hamstrung" and does not have the power or resources to get to the truth, a scathing report by an influential group of MPs has said.

The Independent Police Complaints Commission (IPCC), which is currently investigating the Hillsborough disaster in the UK's biggest-ever inquiry into police misconduct, should be given a statutory power to require a force to implement its findings, the Home Affairs Select Committee said.

More cases should be investigated independently by the IPCC instead of being referred back to the original police force on a "complaints roundabout".

The watchdog, which was established in 2004 and is chaired by Dame Anne Owers, investigates the most serious complaints against the police, as well as the Serious Organised Crime Agency, Her Majesty's Revenue and Customs and the UK Border Agency. A total of 31,771 officers were subject to a complaint during 2011/2012 and when appeals were made against the way forces handled a complaint, the IPCC found that the police had been wrong in one in three cases.

Committee chairman Keith Vaz MP said: "When public trust in the police is tested by complaints of negligence, misconduct and corruption, a strong watchdog is vital to get to the truth - but the IPCC leaves the public frustrated and faithless."

The watchdog should have a statutory power to force implementation of its findings and in the most serious cases it should instigate a "year on review" to ensure that its recommendations have been properly carried out, the committee said.

A Home Office spokesman said: "Improving police professionalism and integrity are at the cornerstone of the sweeping reforms we are making to the police force, and the IPCC has a key role to play. We are already working to ensure the organisation has the powers and resources it needs to manage the challenges it is currently facing and we will shortly announce a package of new measures designed to further improve the public's trust in the police."

Shadow home secretary Yvette Cooper said: "The Home Affairs Select Committee is right that the IPCC is not strong enough to tackle the problem when policing goes wrong. That is why I called for radical reform of police accountability last year, including replacing the IPCC with a new Police Standards Authority."

The IPCC welcomed the committee's report, saying it had already highlighted many of the recommendations and agreed that it could not meet the public's expectations without further resources and powers. Dame Anne said: "This report recognises that we do not yet have the resources or powers to do all that the public rightly expects and needs from us. That is what we have been saying for a long time. Without that, we will continue to struggle to meet the legitimate expectations of complainants and of families who have lost someone in tragic circumstances."

She continued: "We want to be able to carry out more independent investigations. We need to exercise rigorous oversight over the way police deal with complaints, and follow up our own recommendations."