Boris Johnson has conquered Switzerland. The mayor of London entered the alpine republic via the pages of the Christmas edition of Weltwoche, a magazine published in Zurich. Seldom has a "hearts and minds" campaign met with such immediate success. In his interview with Weltwoche, Johnson called for the creation of a new place called "Britzerland". He hopes Britain and Switzerland will become founder members of "a new outer tier of the European Union", which will enjoy free trade with the euro area and have the right to help set the terms of that trade, while opting out of every other integrationist masterplan drawn up in Brussels.

Swiss newspapers at once picked up the story. It is not every day the hand of friendship is extended to their country. More common is the cheap contempt expressed by Orson Welles when he played Harry Lime in The Third Man: "In Switzerland, they had brotherly love, they had 500 years of democracy and peace – and what did that produce? The cuckoo clock."

Let us leave on one side the point that cuckoo clocks are actually produced in the Black Forest, which is in Germany. Switzerland's tradition of sturdy independence does not always meet with the admiration it deserves. Often it is treated with unthinking scorn. Earlier this year David Cameron urged that Britain should not "just withdraw" from the European Union "and become a sort of greater Switzerland".

The subtlety of Johnson's position lies in the fact that he too is against withdrawal. As he put it during the interview, which I conducted for Weltwoche in his office at City Hall, he has always been seen by hardline Eurosceptics as "incorrigibly wet" on the issue of our EU membership. The mayor observed that it "would be taken badly by foreign investors if we were seen to be excluding ourselves from a massive free-trade area". As long as we can negotiate a new relationship with the EU, under which we stay in for trade but opt out of everything else, Johnson will campaign for a yes vote in the referendum, which he wishes to see.

One way to describe this policy is: having your cake and eating it. Experts dismiss Johnson's proposal as incorrigibly unrealistic. But democratic politics often amounts to the assurance, given with varying degrees of sincerity, that we can have our cake and eat it. And one of the merits of Johnson's position is that it reflects what large numbers of both the British and the Swiss actually want to see. We would like very much to retain the right to run our own affairs, while also trading freely with our neighbours.

Johnson thinks Norway and Sweden might like to join Britzerland in the outer tier of the EU. He declined to follow my suggestion that the German public might be interested too. Yet during the six years that I spent in Berlin in the 1990s, I could not help being struck by the affinities between British and German public opinion. These were the years when Chancellor Helmut Kohl defied his own people by driving through the replacement of the Deutschmark with the euro. Just as the British wish to keep the pound, so the Germans wanted to keep the mark.

Johnson now believes the "Procrustean nightmare" of forcing a single currency on widely divergent economies could last until after next year's German elections. But he still maintains that the euro "will eventually blow up". At that point we shall need a new idea of Europe, in which we still know how to get on with our neighbours, while preserving our own democracies. We shall need a Europe which is a club of nation states: a truth that applies as much to the Germans as it does to the British, the Norwegians and the Swiss.