In the past half-century only two continental politicians have ever found themselves in a position to have a major positive influence on the British relationship with Europe. The first was Jacques Delors, the European commission president whose speech to the TUC conference in 1988 was pivotal in persuading Labour leaders and voters to embrace a social Europe in which some of the workers' rights that were being dismantled by the Thatcher government could be re-established on a European scale. Such was the impact of the Delors speech that it provoked a chorus of Frère Jacques from his audience.

The second is Angela Merkel. Tomorrow Merkel pays an important if brief visit to London, and it is generally being reported in the narrow context of the Conservative party's internal management of the EU issue. The German chancellor is far from being an irrelevant player in that partisan context. That is, after all, largely why the red carpet is being so ostentatiously rolled out for her by David Cameron.

But Merkel is also in the position, should she want it, to play a tantalisingly influential role in the wider British debate about Europe. If she chooses to grasp that opportunity, and if she does it well and consistently, she could be more influential than Delors in shifting UK attitudes. But is that what she wants?

We should not get ahead of ourselves. Today's visit is not Merkel's date with British destiny, and is being hyped far beyond its immediate significance. Merkel's invitation to address a joint meeting of both houses of parliament, followed by an audience with the Queen at Buckingham Palace, marks the chancellor as a political A-lister. But she is not getting the ultimate accolade – granted to Nelson Mandela, Aung San Suu Kyi, Barack Obama, or her countryman Pope Benedict – of giving a joint address in Westminster Hall. Instead, like Willy Brandt 44 years ago, Merkel gets to speak in Westminster's Royal Gallery, where a painting of Wellington meeting Blücher at Waterloo – a great Anglo- German achievement of yesteryear, the work of Maclise – looks down on her.

More important than the protocol is the stubborn fact that Merkel's visit cannot possibly deliver what Cameron wants it to. Number 10 has marked Merkel down as the Tory leader's most important potential ally in his attempts to deliver a "yes" vote in the referendum about Britain's renegotiated EU membership he hopes to hold in 2017. But although there is a common Merkel-Cameron interest in British membership, the massive gulf over Europe between the two leaders has not suddenly disappeared.

Yesterday, it was reported that Merkel is ready to offer Britain special opt-outs in any revised EU treaty, strengthening the institutions and harmonising the processes of the eurozone countries. That would be good news for Cameron if it were to happen. But it was simultaneously reported that Merkel's speech will call for a much more effective EU, stressing that changes must be carried out in order to strengthen – not weaken – the EU as a whole. That might not suit Cameron quite so well.

This gulf is exceptionally hard to bridge. Merkel wants a stronger EU with more shared approaches and bigger global clout. Cameron actually wants the opposite – a weaker EU with much greater internal flexibility that plays only a limited role on the world stage. Each position reflects the respective politics of the two nations.

Germany is comfortable with the idea of subsidiarity – decision-making at the most appropriate level. This reflects Germany's long simultaneous commitment to regional, national and European levels of decision-making. Britain, on the other hand, takes something closer to a zero-sum approach: the more power resides in the nation state, the less that can be allowed to either local government or the EU.

Then there is a further unignorable gulf: Merkel may not be the most committed proponent of her country's social market model in modern German history, however, her CDU party retains a distinct place for the social dimension in its vision of what a good Germany and a good Europe should look like. Look at her government's programme if you doubt that.

In any case, Merkel also leads a coalition government with a social democratic party that would not countenance the scrapping of the EU's social dimension. Yet that is fundamentally what Cameron and most modern Tories seek to do – to roll back the Delors settlement and leave Europe as a single market with as few social commitments as possible.

That is not to say that Merkel and Cameron would not be able to agree a package of EU competences. But it cannot spurn social Europe. It must, after all, also be sold to the EU's 28 members. So unless the two governments were better able to share a public commitment to where this was all leading, an accord might not last long. In practice, that can only mean the Conservative party leader openly committing to the long-term desirability of Britain participating as effectively as possible in Europe, social dimension and all, not to a grudging "OK, we're staying – but now leave us alone". But who expects that to happen in the modern Tory party?

The crucial test for any Cameron-Merkel project for Britain and Europe would be whether both sides could deliver on their side of any bargain. Both would find it difficult, particularly Cameron. Merkel has no incentive to start offering concessions this side of a UK general election that Cameron may not win. And even if he does win, a large part of his party wants to quit Europe anyway and under all conceivable circumstances. Tragically for the Tory party, Cameron has never shown great bravery on this issue. Who can suppose that this self-described Eurosceptic is suddenly going to change and become, at the eleventh hour, the new Heseltine that the Tory party so clearly needs?

Which leaves the question of Merkel's role. If she seriously wants to intervene in the British debate about Europe – and not just to do her bit in the Tory party's manoeuvrings – Merkel could make a huge and positive difference. She would need to pick her moments – a speech to the CBI or the TUC in 2015, perhaps, or a Dimbleby lecture then or in 2016. But if she – the only widely admired European politician of the age, leading what is the most admired European nation of the modern era – was to set out her vision of the new Europe and Britain's role in it, the British argument over Europe might suddenly look and feel very different indeed. She has our future in her hands.