There is a strong sense of a change in the political weather in Westminster. Between them, the slump back into recession and the Rupert Murdoch saga are a potentially deadly combination for a Prime Minister and a Chancellor already showing signs of fragility after a badly received Budget and their spectacular mishandling of the looming fuel strike.

Of the two issues that exploded this week, the bad economic news is the more significant. The Coalition was formed, above all, with the aim of reviving Britain's fortunes in the aftermath of the financial crash. Yet the economy was growing when David Cameron came to power and has been in decline ever since. While Labour claims this week that the recession was made in Downing Street are an exaggeration, Mr Cameron and George Osborne will find it ever more difficult to blame their predecessors for the economic storms they face. While the Coalition enjoyed the benefit of the doubt, voters showed a willingness to endure the pain of public spending cuts. A return to recession not only makes it harder to win the argument on deficit reduction, but it also makes it more difficult for ministers to take further tough decisions on spending.

In Britain, the fate of governments is more often than not determined by the economy. The only striking exception to this rule was the 1997 election: although the economy was growing fast, John Major's Conservatives were almost wiped out by a string of stories about sleaze. In the past week, Mr Cameron has had to face both at once: the latest GDP figures indicating a relapse into recession coming just one day after new allegations of sleaze in his relationship with Rupert Murdoch.

Like every prime minister since Margaret Thatcher, Mr Cameron has wooed Mr Murdoch and his senior editors assiduously. What makes this relationship more potentially toxic is the BSkyB deal. The Culture Secretary, Jeremy Hunt, is still clinging to office, but only with a plea that his case be put to the Leveson Inquiry, rather than with an explanation of the mountain of emails between his former adviser and News Corp. And when Mr Cameron himself takes the stand at Leveson, the claims from James Murdoch this week that he did indeed talk to the Prime Minister about the BSkyB deal – albeit briefly – will return to haunt him.

With a rash of local elections and the mayoral contest in London next week, voters will have an opportunity to give their verdicts on recent developments almost immediately. The national dramas are bound to have some impact on voting patterns, but perhaps not as much as they used to do. The most high profile of next week's ballots is the London mayoral race. But while polls suggest that Labour is well ahead in the capital overall, Boris Johnson has a lead over Ken Livingstone when it comes to the mayoralty. Similarly, Labour's national poll lead made no impact in the recent Bradford West by-election snatched by George Galloway.

The possibility of local aberrations can be of only limited comfort to Mr Cameron. If Mr Johnson wins in London, his victory will be seen as a personal triumph secured in spite of the Government rather than because of it. And although Mr Cameron will be able to argue that Labour is not sweeping the country in electoral tests, the challenges facing Ed Miliband's party are already a familiar part of the political landscape, as are the travails of the Liberal Democrats.

More than anything else, the problems that have beset the Government since the Budget are a crisis for the leadership of Mr Cameron and Mr Osborne. Even their own party are increasingly on the attack, and Nadine Dorries' suggestion that the duo are out-of-touch "posh boys" is starting to resonate dangerously.

True, apparent turning points halfway through a parliament often prove illusory. Recent electoral history is littered with examples of opposition mid-term leads that come to nothing. But with their economic strategy under increasing pressure, and the Leveson Inquiry far from over, Mr Cameron and Mr Osborne would be unwise to assume their recent rough trot is merely a bout of fleeting mid-term blues.