The Commons has passed a motion to force the publication of secret texts and emails relating to Covid PPE contracts secured by a company linked to Conservative peer Michelle Mone.
But ministers will release the documents when investigations have finished, the government said.
Health minister Will Quince told the Commons the administration was “committed” to producing the information on PPE Medpro.
But he added that would happen when “all investigations are concluded”.
Labour’s deputy leader Angela Rayner had told Tory MPs they would be “complicit in a cover-up” if they voted against the motion, which called for the publication of all communications by ministers or advisers with the controversial company.
In the end, they abstained and the motion passed the Commons unopposed.
Baroness Mone has come under growing pressure since it was reported that she is a beneficiary of an offshore trust believed to have received £29m from PPE Medpro’s profits.
A House of Lords standards inquiry into allegations she failed to declare an interest in the company has been put on hold while a police investigation takes place.
The former lingerie entrepreneur, ennobled by David Cameron in 2015, has previously denied benefiting financially and has claimed she “was not connected to PPE Medpro in any capacity”.
She is to take a leave of absence from the House of Lords to “clear her name” over the allegations.
But Rishi Sunak has faced accusations of weakness over his failure to withdraw the Tory whip from the peer.
Labour’s motion was in the form of a “humble address” to force the release of “all papers, advice, and correspondence involving ministers and special advisers” to the cross-party Commons public accounts committee.
Such an address has been successfully used in the past to force the release of documents by the government.
Earlier this week former health secretary Matt Hancock claimed Lady Mone had aggressively lobbied him on behalf of another company in a row over a different set of contracts last year.
In his diaries he wrote: “Baroness Michelle Mone has sent me an extraordinarily aggressive email complaining that a company she’s helping isn’t getting the multimillion-pound contracts it deserves.
“She claims the firm, which makes lateral flow test kits, ‘has had a dreadful time’ trying to cut through red tape and demanded my ‘urgent help’ before it all comes out in the media. ‘I am going to blow this all wide open,’ she threatened.”
PPE Medpro was awarded two contracts without tender for masks and gowns with a total value of £203m in 2020, but the gowns were never used after failing NHS quality checks.
After the motion passed Ms Rayner said the government had “finally been shamed into conceding the release of these documents. Ministers must now confirm when, where and how this information will be released. This cannot be yet another Tory whitewash.”
She added that Mr Sunak “must act now to close the loopholes, ban VIP lanes, and give us our money back”.
Liberal Democrat Cabinet Office spokesperson Christine Jardine said: “Transparency is imperative, but it’s no longer enough to just publish these contracts; we must ban VIP lanes altogether so this cannot happen again.”
