In a sudden blast of what feels like old-school politics, Labour has had a go at private schools.

According to Tristram Hunt, the shadow education secretary, the independent sector is not doing enough to break down what he calls the corrosive divide of privilege; he also says private schools should be doing much more to justify their charitable status (and the juicy tax breaks that come with it) by working more closely with state schools.

Similar arguments have been bubbling away in Scotland, where the charitable status of private schools has come under considerable scrutiny, most recently at Holyrood last month when the petitions committee heard calls to end the status entirely. But this week's sudden attack by Labour on private schools should be treated with the utmost suspicion.

For a start, Mr Hunt is a private school boy himself and turning on the independent sector has the slight smell of class shame about it, but worse than that, it looks like a clumsy attempt by Labour to reconnect with working-class voters after the Emily Thornberry flag affair. In tweeting the picture of that house in Rochester, Ms Thornberry was criticised for reacting in a way that most of us react (if we're honest) when we see a house draped in flags. But it left the impression Labour was out of touch with its core vote and so it has had to get back to bashing the middle and upper classes instead of the working class - and what better way to do that than to attack private schools?

The problem for Labour is that, in launching the attack, the party has come to the wrong conclusions. One positive is Mr Hunt does at least appear to accept private schools have the right to exist, which puts him in line with the political consensus. No party, not even the SNP, supports banning private schools, possibly because they realise it's more trouble than it's worth, but hopefully because they recognise that in a modern, liberal society, we should have the right to send our children to private schools if we want to, and can afford to.

The charitable status of such schools is another matter entirely. Most of us know what a charity looks like and it isn't a big building with nice middle-class children pouring into it. And yet independent schools in the UK can still claim to be charities, largely through offering a few places to children whose families can't afford the fees.

Recently, to explore the issue further, I went back to my old school in Aberdeen, Robert Gordon's, which is fee-paying, and spoke to the headmaster there. Unsurprisingly, he defended its charitable status, saying "we are a charity and have been for 250 years", but there was nothing I saw during my visit to the school that justified the status.

Weirdly, Labour appear unwilling to accept this truth, in England or Scotland, where the charitable status of private schools is a matter for Holyrood. Instead, they rabbit on about toughening up the charitable test, as Mr Hunt did yesterday. Private schools, he said, should do more to help state schools, by for example lending out teachers in some specialised subjects.

A more honest approach would be to remove the charitable status entirely, not as part of some attack on private schools but rather as a way of helping them to behave more instinctively. They could get on with educating the five per cent of the population who go private without having to make half-hearted attempts to meet the charitable test, and state schools could look to government rather than private schools for help (why can't state schools be given tax relief for example?).

Interestingly, there was a young Labour party worker I spoke to when I visited my old school, who appeared to have a better grasp of all of this than Mr Hunt does. The party worker was a pupil at the school but volunteered to work for the party in his spare time and he told me that a failing state school should be the responsibility of the state and not the private sector. Perhaps Mr Hunt could give that 18-year-old Labour party worker a call and start a more honest discussion about the party's education policy and in particular the role private schools can and should play in a modern society.