An investigation has begun into the use of taxpayer-funded grants by the charity set up to lead David Cameron's "big society" initiative.

The Charity Commission was examining whether funding for a childhood obesity project was used to pay the debts of a linked company, the Independent reported on Saturday. The commission was also seeking more information on payments allegedly made for consultancy services to two directors of the Big Society Network (BSN) and its chair, Martyn Rose, a Conservative Party donor.

News of the investigation comes days after a public spending watchdog issued a critical report about how National Lottery and government funds were handed over to and used by the BSN.

In a separate incident, a former trustee of one grants body has claimed it was "forced" to award a total of £480,000 to the BSN without undertaking the usual checks.

The shadow civil society minister Lisa Nandy said she was asking the cabinet secretary to investigate whether political pressure was exerted to secure money for ministers' "pet projects".

The BSN was launched by the prime minister at 10 Downing Street two months after the coalition took office, with the aim of encouraging the kind of community work and volunteering Cameron had put at the heart of the party's manifesto for the election.

The performance of many of its projects has been heavily criticised and the National Audit Office (NAO) exposed problems with how £2m worth of grants were handed over to it.

The NAO said the Big Lottery Fund failed to challenge the BSN's "ambitious" target to recruit a million members a year to one particular initiative, despite the meeting of that target being crucial to its success. The Your Square Mile project was given an £830,000 lottery grant, but attracted only 64 members. The grant was also allowed to be transferred to a new company set up by the BSN chairman and another director, without checking that it had the IT skills to make the scheme work, the NAO said.

Its report also found that the £300,000 childhood obesity grant was made "contrary to the Cabinet Office's own guidelines" and even though it did not meet its criteria for funding.

The Independent reported that officials had been told to "go back and change the criteria".

The funding was halted after £200,000 had been handed over because of the project's poor performance, and the Cabinet Office did not recoup any of the funds.

Civil Society News reported that, in a separate incident, £480,000 was handed over to the BSN by the innovation funders Nesta, now a private organisation but then a quango, without a competitive pitch.

One of its former trustees, Liam Black, has said it was "forced" to hand over the resources for setting up BSN and several projects, branding it a "scandalous waste of money".

Nesta told Civil Society News: "While the vast majority of Nesta's grants are made following open calls for proposals, we do have the ability to provide grants to projects that fit with our vision and advance our objects outside of open calls for proposals. That is what happened with the grants to the Big Society Network."

It said in a statement that the grants to the BSN were approved by Nesta trustees "following a thorough review and proper consideration", and that it did not fund any of the projects highlighted in the NAO report.

A Charity Commission spokeswoman confirmed that it was examining the award and use of funds by the BSN's charity arm.

"Our case into the Society Network Foundation remains open and ongoing," she said.

"We have received a response to questions we had relating to connected party transactions and the use of a grant, however this does not fully address our concerns and we are in the process of engaging further with the trustees.

"We are also awaiting copies of documents that explain the grounds on which a grant was given."

Rose, who the Independent reported had contributed more than £54,000 to the 2010 Conservative election campaign, told the newspaper he did not recall the payment from the network but said tit was possible that "one of my companies did work on its behalf".

He said he put £200,000 of his own money into the Big Society Network, which he had not got back, and defended its operations.

"With hindsight, of course, if we had all known that the projects were not going to work we would have been idiots to do them," he said. "In the early stages of social investment some will work and some won't."

Nandy said the entire big society project lay "in tatters" and called for an investigation.

"It's bad enough that millions of pounds of public money were squandered, but the connections between these organisations and the Conservative party are deeply concerning," she said.

"I am writing to cabinet secretary Jeremy Heywood to ask him to investigate the process by which the grants in question were given.

"We must know if political pressure was applied to give an organisation with close ties to ministers special treatment.

"At a time when many charities are fighting to survive, handing out large sums of money to flawed, pet projects is inexcusable."

A Cabinet Office spokesman said: "The awarding of this grant has been the subject of intensive investigation by Cabinet Office and independently by the NAO.

"Both investigations found no rules were broken and the matter is now closed."

• This article was amended on 29 July 2014 to clarify that the case involving Nesta is separate to those investigated by the National Audit Office and the Charity Commission.