British politicians still prize a visit from the President of the United States above all others. Yet no American President has been as important to a British Prime Minister, in domestic political terms, as the German Chancellor is to David Cameron. Angela Merkel is the person who can both help him keep his party together as it approaches the next election and then, with luck, deliver his promised renegotiation of Britain’s EU membership. For Cameron, Merkel — far more than Barack Obama — is the indispensable ally.

When Merkel comes to London next week, Cameron will roll out every available inch of red carpet. Though she’s here for just a day, she’ll address both houses of Parliament and meet the Queen.

All the buttering up serves a purpose. No. 10 is confident that Merkel will use this trip to offer some encouragement to Cameron’s renegotiation agenda. One source involved with the visit says, ‘She knows everyone will be analysing her words, she is coming to be helpful. She has gone out of her way to ease the path for the PM.’

Support from Merkel is crucial because her word carries more weight in Europe than anyone else’s. The eurozone crisis has confirmed that the Franco-German partnership is not one of equals. Germany, with the biggest economy and the deepest pockets, is the dominant force in the European Union. As one Foreign Office figure puts it, ‘In today’s Europe, you can’t change things unless Germany is with you.’ Even if Britain were to leave the EU, Merkel and Germany would determine the exit terms.

If Cameron can show that Merkel is at least sympathetic to his renegotiation plan, he’ll be able to credibly claim that his strategy has a chance. So keeping Merkel sweet is now one of the defining features of Cameron’s European policy. This government has quadrupled the number of ministerial and official visits to Germany. Word has gone out across Whitehall that ministers and permanent secretaries must visit Berlin as regularly as they do Washington or Paris.

The charm offensive goes beyond diplomatic courtesies. Last autumn a question arose about new EU pollution limits for cars. The Business Secretary, Vince Cable, and the Energy Secretary, Ed Davey, were in favour. Germany, which still has a large car industry, wanted a delay. We went with Germany. London will also fall in behind Berlin over what to do about Switzerland, which has voted to end immigration rights for EU citizens.

There are substantive reasons why Merkel should want to help Cameron with his European mission. Germany wants an open, competitive, free-trading EU; in that aim, Britain is a useful ally. And Merkel sees Cameron as one of the only other European leaders to grasp the existential crisis facing the continent. He shares her concern that Europe accounts for 7 per cent of the world’s population, 25 per cent of its economic output and 50 per cent of its social spending.

It helps that the two leaders get on. Tales of friendship between heads of government are often dismissed as irrelevant or confected. But at the very top of European politics, the personal is political. It is widely understood that Silvio Berlusconi would not have been ousted as Italian prime minister if he had got on with Merkel.

Cameron and Merkel’s relationship got off to an awful start when, as opposition leader, he withdrew his party from the centre-right grouping in the European Parliament. In office, however, the pair have bonded. Merkel has, as one Cameron ally put it, a ‘very long memory’. But she and Cameron are both pragmatists who roll their eyes at the histrionics of other European leaders. Each has interests outside of politics, though Cameron’s cultural hinterland is less elevated than Merkel’s love of Wagner.

At this point, government advisers are more familiar with parts of the German co-alition agreement — in particular, the commitment to EU treaty change — than with some corners of their own. They gleefully reel off the emerging areas of Anglo–German consensus on European reform. Berlin shares London’s desire to make it harder for people to move to another country and instantly access benefits. It agrees that far longer ‘transition controls’ must be imposed before the citizens of any new EU member state can benefit from freedom of movement. And do you remember William Hague’s idea that national parliaments should have a veto on EU laws? Merkel’s CDU party is about to embrace it.

But this package will not be enough on its own to make the bulk of the Tory party support staying in the EU. The Cameroons must remember that, for all Merkel might want Britain to stay, she will not, as one Foreign Office source cautions, ‘throw overboard some key German interest to achieve that’.

Even if Merkel is prepared to be the answer to all Cameron’s European prayers, that might yet be a problem in itself. Her power is now at its zenith, and he needs her to be as strong when the renegotiation nears its conclusion in two years’ time. But she is not expected to run for re-election in 2017, and once she’s a lame duck, Germany may tilt back to its more traditional integrationist position. One Cameron confidant dismisses this suggestion: ‘She has a history of cutting the legs off people who set themselves up as rivals.’ Still, Cameron remains alarmingly dependent on Merkel. His whole EU strategy turns on this relationship.

Then there is the perennial danger that the Franco-German axis will reassert itself. Merkel and Hollande are not simpatico either personally or philosophically. But history suggests that, forced to choose, Germany will pick France over Britain.

Cameron is right to be heaping honours on Merkel: every little helps when it comes to diplomacy. But there is a real danger that he isn’t leaving himself enough time to come up with a deal that will really change Britain’s terms of membership and placate his own party. He urgently needs to cultivate European leaders other than Merkel. His meeting with the Dutch Prime Minister this week should be the start of a sustained Cameron effort to bring other northern European reformists on board. Merkel’s support is necessary but not sufficient for a new deal.