Cameron was summoned to answer lawmakers' questions about his efforts to win government funds for Greensill Capital.
The former Conservative Party leader is a key link in a chain of contacts between government ministers, civil servants and Greensill, which collapsed in March.
The bankruptcy forced the owner of Liberty Steel, which employs about 5,000 people, to seek a bailout.
"In the end substance is what matters (help for SMEs) - the form can always be sorted", one message from Cameron to Sunak said.
Cameron, who told the committee his evidence marked a "painful day", reserved much of his contrition for the casual nature of his lobbying messages, saying he should have opted for a "more formal approach" than text messages to old colleagues.
"There was certainly no sense of jeopardy" at board meetings, he said.
Cameron denies having broken any rules which state that "on leaving office, ministers will be prohibited from lobbying government for two years".
Cameron contacted Cabinet Office Minister Michael Gove and Vaccines Minister Nadhim Zahawi - who was then business minister, asking them to help get a government-backed COVID-19 pandemic emergency loan for Greensill Capital, of which he was an adviser and holder of share options worth up to £40 million.
And referring to his involvement in the Earnd app used in the NHS to allow staff to receive payments up-front, she asked him: "Do you accept that your lobbying of the NHS wasn't for its health but for the health of Greensill expand its balance sheet?"
In documents published Tuesday by the committee, the ex-prime minister and his office staff sent ministers and officials dozens of emails, texts and WhatsApp messages a year ago relating to Greensill, bypassing official channels. He said that did not necessarily indicate a close relationship. In subsequent messages, Cameron said he was "genuinely baffled" by the decision, calling it "bonkers", "nuts", and probably down to a "simple misunderstanding that I can explain". "My children tell me that you don't need to sign off text messages at all and it's very old-fashioned and odd to do so".
"There are lessons for me to learn and in future the single formal email or letter would be more appropriate".
The former prime minister admitted he was paid a "generous annual amount" which was "far more" than he earned in Downing Street as he faced questions from the powerful Commons Treasury Select Committee.
The collapse of Greensill has sent shockwaves through its customers, with speculation that some of them may go out of business, putting thousands of jobs at risk.
Cameron potentially stood to make millions if Greensill went public.
It meant that Mirabella had the responsibility to ensure that Greensill was playing according to the rules, while Greensill itself was not regulated by the Financial Conduct Authority (FCA).
"I've sat on the other side of the fence in government, where you have a credit crunch, you have difficulties in the credit market, and you're desperate to get banks lending", he said.
He said he had a "serious economic interest" in the company via shares, but claimed the exact amount he was being paid was a "private matter" and fear of losing money was "not what motivated" him to lobby ministers.