LONDON — Until last month, David Cameron was known for one big thing: calling the referendum in June 2016 that produced Britain’s shock vote to leave the European Union and triggered a political earthquake that toppled him as prime minister.

Now, Mr. Cameron is in the headlines for something else: the spectacular collapse of a high-flying Anglo-Australian finance firm. His lobbying on behalf of the firm, Greensill Capital, does not appear to have violated any laws, but it has added another blot to an already checkered legacy.

Greensill’s access to senior British officials — aided by Mr. Cameron, who worked for the firm — has set off a noisy debate about the rules on lobbying by former leaders; critics say they are woefully inadequate. It has also turned a fresh spotlight on a recurring theme in Britain: the challenging after-lives of British prime ministers.

From Margaret Thatcher to Tony Blair, occupants of 10 Downing Street have often struggled after leaving office, an abrupt transition to private life that leaves them without the trappings of power, no clear public role, and little financial support. For politicians used to privilege and influence, analysts said, it can lead to trouble.

In Mr. Cameron’s case, he began working for Greensill Capital in 2018, according to the Financial Times, which said he stood to make up to $70 million in share options. The collapse of the firm has rendered those worthless. The paper also reported that Mr. Cameron traveled to Saudi Arabia with the firm’s founder, Lex Greensill, where the two camped with Crown Prince Mohammed bin Salman.

The Times of London reported that Mr. Cameron sent text messages to the chancellor of the Exchequer, Rishi Sunak, urging him to approve loans to Greensill, a supply-chain financing company. Mr. Sunak did not act on the requests, but questions remain about why the firm got as much access as it did.

Mr. Cameron did not respond to a request for comment, conveyed through the publisher of his book, HarperCollins, which forwarded it to his office.

Greensill’s collapse has reverberated around the world, nowhere more dramatically than in Britain, where it has jeopardized the business empire of the steel tycoon Sanjeev Gupta. Given the huge stakes involved, Mr. Cameron may end up with little more than a cameo role in a global drama. Restrictions on lobbying by former officials apply to outside lobbyists, not those working as employees of the company.

“He’s broken no rules, and in a way that’s the problem,” said Bronwen Maddox, director of the Institute for Government, a think tank in London. “It looks wrong for someone so recently in office to use his influence this way. There need to be clearer rules for a longer period after a prime minister leaves office.”

For all the questions about Mr. Cameron’s dealings — to say nothing of his miscalculation on Brexit — he does not arouse the hostility that many in Britain still feel toward Mr. Blair over his backing of the Iraq war. Much of the media coverage has portrayed Mr. Cameron as a decent man guilty of poor judgment.

Ms. Maddox said his case underscored that “Britain should do more to help prime ministers forge a useful life afterward.”

Unlike American ex-presidents, who get taxpayer funded offices and can busy themselves building their presidential libraries, prime ministers have little in the way of a soft landing after they leave office. The rough-and-tumble nature of British politics means that many are defenestrated — one moment, at the helm of a nuclear state; the next, exiled to the parliamentary backbenches.

Mr. Cameron announced his resignation hours after Britons voted narrowly to leave the European Union, an outcome he campaigned against. At his last appearance in Parliament, he declared, “I was the future once,” a rueful play on a jibe he once aimed at Mr. Blair, when Mr. Cameron was the rising leader of the Conservatives and Mr. Blair a Labour prime minister in the twilight of his career.

“When you’re in politics, every day is a thrill or a spill,” said Simon Jenkins, a columnist at the Guardian. “Then you’re out, almost invariably because of a great mistake. You’ve got nothing to do, and nothing you can do.”

Only 49 years old when he left office, Mr. Cameron wrote a memoir, for which he was paid a reported advance of 800,000 pounds ($1.1 million). He joined several boards and became the president of an Alzheimer’s charity. He plays tennis regularly at a club near his house in West London. In 2017, Mr. Cameron’s wife, Samantha, started her own women’s fashion business.

A well-pedigreed graduate of Eton and Oxford, whose father was a stockbroker, Mr. Cameron is wealthy by conventional yardsticks. But his fortune is less than that of Mr. Blair, who amassed real estate and established a lucrative consulting business. Mr. Blair’s money-raising activities drew criticism as well, especially his work on behalf of the repressive government of Kazakhstan.

Mr. Cameron’s friends have described him as thriving on the speaking circuit and not hung up about his financial circumstances. In “Diary of an MP’s Wife,” a gossipy account of Conservative Party social circles by Sasha Swire, the wife of a former Conservative lawmaker, Hugo Swire, Ms. Swire wrote that in 2017, Samantha’s business was “taking off and Dave is making loads of money.”

“He says every time he looks for a loophole to stash it away, he realizes that George and he closed it, and laughs,” Ms. Swire added, referring to George Osborne, who was Mr. Cameron’s chancellor of the Exchequer.

Ex-prime ministers, however, have far less earning power than ex-presidents. Barack and Michelle Obama signed a $65 million multi-book deal with Penguin Random House and earned millions more in a production deal with Netflix. Bill and Hillary Clinton earned $139 million from 2007 to 2014, mostly from speeches and books. George W. Bush has also earned tens of millions from speeches.

Like presidents, prime ministers become accustomed to mingling with extremely wealthy people, Mr. Jenkins said, leading them to question “why they’re an ex-prime minister when they could have been a wealthy tycoon.”

Not everyone who vacates Downing Street has struggled. John Major, Ms. Maddox said, has arguably been more successful as an elder-statesman commentator than he was in office. Theresa May, who succeeded Mr. Cameron and resigned in 2019 after her efforts to strike a Brexit deal failed, stayed on in Parliament as a Conservative backbencher and has weighed in on debates at key moments.

“It’s a rightly informal system here,” said Charles Moore, the author of a biography of Mrs. Thatcher. “If you cannot command a majority in the Commons, you’re out. That is democratic, and you should then, with a little help over the immediate transition, make your own way in the world.”