Labour has called for the investigation into the conduct of Liam Fox to be widened to include all ministers to make sure no one else in government has behaved the same way.
Shadow defence secretary Jim Murphy said that that Fox's resignation on Friday was "not the answer to the problem" and warned there were "wider lessons to be learned".
Fox has been replaced by former transport secretary Philip Hammond following his resignation as defence secretary.
He left the Ministry of Defence after allegations that he allowed Adam Werritty, a close friend who did not hold an official job, improper access to government.
Werritty has passed himself off as an adviser to Fox, including handing out business cards, but he had not been security cleared not was he subject to public scrutiny in the same way official political advisers to ministers are.
The cabinet secretary, Sir Gus O'Donnell, is due to report back early next week as to whether Fox broke the ministerial code. It is expected to be critical of the former defence secretary, leading some to speculate that he left office before he was forced to in order to secure a more dignified exit.
For days David Cameron had insisted he would await the outcome of that review before making a decision whether to sack his defence secretary or not.
Revelations in the Friday papers, including a report in the Times that traced the funding of Werritty to wealthy political backers who had not been declared, proved to be the final straw.
But Murphy told the BBC on Saturday that the full truth about where the money came from was still unknown.
"The main thing we've got to do is follow the money, undeclared money, off the books behind the scenes in a shadowy way," he said.
"If we follow the trail of money we will be able to discover who was trying to exert power and influence in very delicate areas of government."
Murphy also said that the inquiry should be expanded to examine the conduct of everyone in government.
"We have to look at the wider issues, to be sure no one else in government has behaved this way," he said. "This morning I'm not sure we have got the full truth yet and we need to get there."
In his letter of resignation delivered to the prime minister, Fox said he was leaving his post with "great sadness".
"I have also repeatedly said that the national interest must always come before personal interest. I now have to hold myself to my own standard," he said.
"I have therefore decided, with great sadness, to resign from my post as Secretary of State for Defence--a position which I have been immensely proud and honoured to have held."
In his reply, Cameron said he understood why Fox was stepping down and expressed gratitude for the work he had done.
"I understand your reasons for deciding to resign as Defence Secretary, although I am very sorry to see you go," he said.
"We have worked closely for these last six years, and you have been a key member of my team throughout that time.
"You have done a superb job in the 17 months since the election, and as Shadow Defence Secretary before that.
Labour's shadow defence secretary Jim Murphy said Fox had brought the crisis on himself.
"I do feel sorry for him as a human being, but he hasn't been brought down by me or the media, he has resigned as a result of a self inflicted political crisis," he said.
Fox's retreat to the backbenches prompted a mini-reshuffle, with Philip Hammond moving from transport to fill the vacency in the Ministry of Defence.
Widely regarded as a 'safe pair of hands', Hammond had been destined to become chief secretary to the Treasury in a Conservative majority government.
But the necessities of coalition meant that role was filled by Lib Dems, first by David Laws and then Danny Alexander.
In a statement following his appointment, Hammond said he would "ensure that our defences are robust and that the finances that lie behind them are equally robust".
Justine Greening, formerly the economic secretary to the Treasury, has been promoted to the cabinet as transport secretary - making her the fifth woman in the cabinet.
And Chloe Smith, the 29 year old MP who won the Norwich North by-election in 2009, takes over Greenings old role as the number five in George Osborne's team.
The promotion of two women will be seen as part of an effort by Cameron to tackle a perceived problem with female voters.
There had been speculation that Cameron may replace Fox with another right-winger, perhaps even bringing former shadow home secretary David David back into the front bench team.
His failure to do so has upset some on the conservative wing of the Conservative Party, who are already unhappy at having to share power with the Liberal Democrats.
Backbencher Peter Bone told Newsnight on Friday that the right wing was now "grossly under-represented" in government.
And he told the BBC that the the backbenches would be "much stronger" now that Fox had rejoined them, expressing hope the deposed defence secretary would help push the government in a more conservative direction.