All politics is local. Or at least that is what they used to say before Brexit.

The old line – usually attributed to one-time speaker of Congress Tip O’Neill – never quite rang true. Sure, in democracies, power is ultimately won at your neighbourhood polling station. In reality, national politics is no more local than local politics is national. No level of government is insulated from another. Everything is linked.

Take Britain’s vote to leave the European Union. This, as a conference heard yesterday, could pose serious challenges for some of the most basic services provided by local authorities.

The leader of Glasgow City Council, Susan Aitken, has asked about her ability to feed children in school or care. Or even to ensure it has enough fuel for its bin lorries, at least in the event of a no-deal, car-crash Brexit. When local politicians tell you Brexit is rubbish, take them literally.

Town halls across the UK have this headache, whether they realise it or not. Like businesses, they will have reached different stages in planning for the worst and hoping for the best.

But should we start thinking about councils’ global roles in a different way? There has been a long tradition of petty local politicking, of knocking “junkets” and questioning local authorities’ international links.

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As the UK Government retreats from its biggest alliance, souring relationships with neighbours and trading partners, can councils step in to keep alive the European spirit? Glasgow thinks so. Scotland’s biggest city, with an EU migrant as lord provost, has made statements about its European-ness.

This isn’t just empty posturing. Scotland’s brand in the EU is not as strong as some Scots like to think. But there is growing awareness of a different, less Eurosceptic politics north of the Border.

So never underestimate soft power, even when wielded by a mere council. The corny old school exchanges and twinning arrangements may just help persuade overseas visitors and investors that Scotland is still Europe. Welcoming noises may help stem net outflows of the migrants Scotland desperately needs to keep public services operating. Image matters.

And what is true for a council is even more true for the Scottish Government. Next time you see Nicola Sturgeon in Europe, remember, she is doing her “day job”.