Short of David Cameron falling to his knees in Downing Street and shining her shoes with his tongue, No 10 really couldn’t have done more to suck up to Angela Merkel. The German chancellor was treated to tea at Buckingham Palace, the poshest caff that Britain can offer. John Bercow, the Speaker, welcomed her to the royal gallery of the House of Lords by trowelling on the flattery before peers and MPs listened in respectful silence to her arguments of substance and laughed deferentially at her dry jokes.

British reporters, normally distinguished by their lack of reverence, were the acme of politeness in their questioning at her joint news conference with the prime minister. The closest we came to a moment of lèse-majesté was when one asked whether it was true that she regarded the man sitting next to her as “a naughty nephew”. The prime minister pinked and gave a schoolboyish snigger. She looked as if someone had offered her a bad sausage. One German journalist even remarked to her that she had been received as if she were “the Queen of Europe”. Contrasts were made, and these contrasts were encouraged by No 10, with the treatment recently meted out to Franois Hollande who was given a pub lunch on a wet day in Oxfordshire and subjected to interrogation about his sex life.

For all this effort to make nice to Angela, what did David Cameron receive in return? Well, the German chancellor clearly appreciates the difficulties that her host has managing his increasingly Europhobic party, even if it is reported from Berlin that she privately thinks much of it has been recklessly self-inflicted by Mr Cameron’s promise of a renegotiation of the terms of British membership followed by an in/out referendum on a timetable to which no one else in Europe has agreed. She did what she could to help him by indicating a few areas where her country could have a common interest with Britain in changing the way in which the European Union works. But on the big, existential question, on the thing that really arouses the passions of the Conservative party, she delivered a rebuff. It was gracefully delivered, but a rebuff it was, and all the more pointed for coming in the part of her speech that was delivered in English. This was the crucial passage: “Supposedly, or so I have heard, some expect my speech to pave the way for fundamental reform of the European architecture which will satisfy all kinds of alleged or actual British wishes. I’m afraid they are in for a disappointment.” The central, animating theme of her speech was to champion the European ideal which has always been so important to post-war Germany and to dash any fantasies that might be entertained by Tory MPs that she would support Britain if it sought to unravel the essential fabric of the EU.

The only surprise is that anyone expected anything different. Merkel is currently Europe’s most successful politician. Those who have seen her in action around negotiating tables report that she is a tough and careful bargainer. One thing you don’t do if you are any good at negotiating is show your hand too early.

Another thing you don’t do is lay out your position before you know with whom you might be negotiating. It is safe to assume that a woman with a doctorate in “the mechanisms of decay reactions and velocity constraints in quantum chemical methods” has some facility at maths. The numbers don’t look too hot for her British counterpart at the moment. She can read opinion polls and they tell her, like they tell everyone, that the Tory leader is suffering from both decay reactions and velocity constraints. There is no guarantee that David Cameron will ever call a referendum on British membership of the EU because there is no certainty that he will still be at No 10 after May 2015. It could be Ed Miliband whom Merkel’s officials will have been briefing her about and whom she took care to meet for private talks during her London visit.

Even if David Cameron is still in Downing Street after the next election, it is not terribly clear which David Cameron she and the rest of Europe will find themselves dealing with. Would it be the Tory leader who has sought to appease his Europhobes by suggesting that he will seek sweeping change to the terms of membership? Or would it be the Tory leader who sometimes implies that he would pursue a more modest new settlement that would be more likely to be palatable to other member states? More than a year has passed since he gave the speech in which he made the referendum pledge and he has yet to detail his shopping list. The reason he fears to do so is because he knows that a substantial faction of the Conservative party will instantly denounce it as too feeble. Some of them want out of the EU whatever might be the outcome of a renegotiation. Others dream of continued membership on such minimalist terms access to the internal market and that is about it that the rest of Europe would never agree.

For some time now, Cameron has relied heavily on the capacity of the German chancellor to come up with enough accommodations and, as importantly, on her ability to persuade the rest of Europe to accept them for him to be able to present a renegotiation as a success and recommend a yes vote in a referendum. From any British government’s point of view, it makes sense to invest in the relationship with Europe’s richest and most politically powerful state. But No 10 has consistently over-estimated both the desire and the ability of the chancellor of Germany to ride to David Cameron’s rescue. Germany has a strong preference for Britain to remain within the EU. Merkel would want to help Cameron win a referendum on continued British membership. But if it was not clear before, no doubt remains after her speech in the royal gallery that she is not going to pay any price to keep Europe’s most truculent member in the club.

For one thing, which often seems to be strangely overlooked in No 10, she too leads a coalition. In her case, it is with the SPD, a party which is at least as Europhile as our own Lib Dems and which will be very resistant to making concessions of substance on social policy.

For another, she appears to be more conscious than her British counterpart that, if there is a renegotiation, it won’t be just the two of them in the room. This isn’t going to be Roosevelt and Churchill drawing lines on maps over brandy and cigars. As she went out of her way to point out, in any negotiation there would be 26 other voices around the table, each with the power to veto any changes to existing EU treaties. David Cameron better get busy buttering up the Cypriots and the Maltese, too.

Some other member states may be aligned with elements of Cameron’s agenda. His people talk optimistically of an emerging alliance of northern European states sharing the prime minister’s desire to give more say to national parliaments, curb the powers of Brussels and make Europe more competitive. Yet even among some of those countries that might be sympathetic there is confusion about what Britain really wants and some anger that a country which already has a fistful of opt-outs is demanding more special privileges.

It is also hard not to think that drawing constant attention to how much the British government admires the German chancellor and how contemptuous it is of the French president is a funny way of going about diplomacy when Mr Cameron is going to need the help of Francois Hollande as well. The repeated snubs meted out to the Frenchman may seem amusing to some people here, but I don’t hear much laughter pealing from the Elyse Palace. Desperately unpopular he may be, but his term as president of France runs to 2017, the year by which Cameron is supposed to have completed his renegotiation and be going into a referendum. Without the co-operation of the French, the prime minister’s plan won’t even get to first base.

He and his people have tried to draw comfort from some of the more optimistic remarks made by the German chancellor at their joint news conference when she expressed confidence that Britain would remain in the EU. “It is not a piece of cake, it will be a lot of work,” she said of a renegotiation, but it was “doable”.

There is scope for a deal between reasonable people involving some reform. I can conceive of David Cameron and Angela Merkel, both essentially pragmatic politicians of the centre-right, striking a bargain which would entail limited changes to existing treaties. I can even just about imagine, if the diplomacy was skilful enough, getting enough other member states on board to seal an agreement.

David Cameron’s fundamental problem is the vast gulf between what other EU states might be prepared to sign up to and what a large segment of the Conservative party are demanding. Even if she wanted to, Angela Merkel cannot bridge that great divide for him. No power on Earth can.

— Guardian News and Media Ltd.