IF there is one conversation I would like never to have again it's the one where a fellow parent bends my ear on the sticky subject of whether to send their child to private school - or the still-stickier topic of how to do it when you've got no money.

I don't know why people want to talk to me about this. Perhaps my English accent makes them think I must have gone to private school (I didn't). Or perhaps it's because I live in Edinburgh, and that's what middle-class parents think about here. Either way, the whole topic makes me want to up sticks and move - not to the charmed catchment area of Edinburgh's James Gillespie's, but farther afield. To Finland.

Finland, a country that in the words of one of my favourite Monty Python songs, and common contemporary political ­opinion, "has it all". More to the point, it has no private schools - aside from a few privately-run religious establishments, whose places are actually state-funded. Finland, which nevertheless excels in the Programme for International Student Assessment (Pisa) surveys. Finland, which also has no school league tables or inspections, so presumably none of those cringy photo-shoots we have when a school that just happens to be in a wealthy catchment area celebrates coming top of the league.

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Of course, Finland isn't perfect - in recent years its Pisa status has dropped a few notches, though it remains well above the UK. But in combining relative excellence with a relaxed, egalitarian approach, Finland does seem to almost have it all.

Finland was on my mind when I read about playwright Alan Bennett's recent comments, made in an essay published in the London Review Of Books. "Private education is not fair," he wrote. "Those who provide it know it. Those who pay for it know it. Those who have to sacrifice in order to purchase it know it. And those who receive it know it, or should. And if their education ends without it dawning on them, then that education has been wasted."

Of course it's not fair - though the advantaged often don't care about fairness. And what's not fair about it is not simply that those who go to private school get a better education - research has shown that state school children tend to perform better at university when compared with privately educated children with the same school grades - but that they are inducted into networks of privilege.

Bennett's comments are refreshing, but what is the solution? It can hardly be argued that banning private schools would make our Scottish education system fair. Even the state system is not so much a postcode lottery as a postcode auction, in which the highest bidders - those who can afford the mortgage in the right areas - win. Last week an Audit Scotland report revealed a wide gulf between the highest and lowest performing pupils in schools, much of which related to area and socio-economic status.

The report was a reminder that private schools are not the sole problem. Perhaps it's not even the education system as a whole that is - though it may play a role in maintaining inequality. After all, it is not clear that it is possible to engineer, through education, a more equal society. While the Audit ­Scotland report does suggest there are some schools in more deprived areas that defy expectations, looking at the majority of figures, one suspects the education gaps exist because the socio­economic ones do.

What I feel I am hearing at the school gates, in the parks, and in the kitchens of Edinburgh is not ambition, but fear. Parents are, of course, terrified by stories about the state of our schools, class sizes, the levels of misbehaviour and disruption. But it's more than that. Social mobility becomes more of a source of anxiety where high or rising levels of inequality exist. And that's where we are at today in the UK.

Many parents are attuned to the economic climate of our times, and even if they don't know the figures and aren't primed with the research of French economist Thomas Piketty, they have a sense that inequality is rising. So when they fret over their kids' schooling it's not an aspirational greed, but a mild terror. They no longer have the hope that their own children will end up better off than them. Rather, in the snakes and ladders of life, they are worried that their kids may land on a snake and slide right down to the bottom of the board.

I'd like to believe there might be a way of creating an education system that would help create a more equal society. But I suspect a more equal education is only possible in an already more economically equal society. Finland is an example of that - though income inequality is rising there too, at a lesser rate.

Ah, Finland, Finland, Finland: the country where I quite want to be.