The Metropolitan police should not be allowed to carry out an investigation into whether it withheld potentially vital information from the public inquiry into Stephen Lawrence's death, the shadow home secretary has said.

Yvette Cooper said the allegations should be passed to the Independent Police Complaints Commission so a "criminal investigation" can be launched.

The government said it would wait for a Met review into whether a secret Scotland Yard report detailing questions about the conduct and integrity of a police chief involved in the Lawrence case was given to the 1998 Macpherson inquiry.

The allegations were revealed last month by the Guardian and on Tuesday it became clear that had led to cross-party concerns.

Former Met commander Ray Adams was questioned at the 1998 Macpherson inquiry about corruption. But neither the Lawrence family nor the inquiry panel were given a report by Scotland Yard containing the intelligence and findings of an investigation by its anti-corruption command.

The investigation, codenamed Operation Russell, raised questions about Adams's conduct in the years before the Lawrence case, informed sources say, while finding insufficient evidence to bring criminal charges. Adams insists it exonerates him and denies any wrongdoing.

Cooper said allegations in the media about the possible role of corruption in the Lawrence case needed independent investigation: "This new information should be immediately referred to the IPCC so that they can pursue a full criminal investigation into these allegations."

Labour said it supported a new public inquiry into allegations that police corruption may have shielded the gang that murdered Lawrence in a racist attack in April 1993.

Home office minister James Brokenshire said the government was waiting for the Met to finish its review before deciding whether a further inquiry is needed. The home secretary, Theresa May, has offered to meet Stephen's mother, Doreen Lawrence, to discuss her calls for a public inquiry, he said.

Brokenshire said May was "treating these issues with the utmost seriousness" and added: "Our judgment is that it is appropriate for the Metropolitan police to investigate the current issues, the allegations in relation to corruption and that once that has been provided that it is absolutely right and proper for the home secretary to consider that and to consider whether a public inquiry is or is not required to provide the necessary reassurance to the public."

The Met says it has been unable, after a month of investigating, to establish whether it passed potentially crucial files detailing investigations by its anti-corruption command to the public inquiry into Lawrence's death, which was held in 1998.

Brokenshire, answering an urgent question in the Commons, said: "Allegations of police corruption must always be taken seriously and investigated thoroughly.

"It is essential that we ensure that the actions and behaviours of any corrupt police officers do not undermine public confidence in the police's ability to respond to, investigate and fight crime."

Labour's Clive Efford, who represents Eltham in south-east London, where Stephen was murdered, accused the police of "bluster and delay", while fellow Labour MP Keith Vaz, who chairs the home affairs select committee, said: "What concerns me is the fact that this is an internal inquiry being conducted by the Metropolitan police."

Labour's Nick Raynsford said: "Nothing less than a genuinely independent examination of these latest allegations will suffice."

The allegations have led to cross-party concern. Conservative MP Gavin Barwell said: "Given how long it took to bring Stephen's killers to justice, is it not important that we get swift answers to these latest allegations in a way that instils public confidence, not just for the sake of Stephen's family, but because of the urgent need to build confidence among BME [black minority ethnic) communities in our police and because a single allegation of corruption or racism against one officer undoes all of the good work that so many officers do on our streets."