Second world war references are hard to avoid in the context of Brexit, so here’s one that actually has something constructive to offer. When Britain was in the midst of war, it was also undertaking wholesale reform of the education system.

The mass evacuation of children from British cities to rural areas laid bare the abysmal lack of education many had received. The government response was the 1944 Education Act, which established what we now call state-maintained comprehensive schools and free, compulsory education to the age of 15. Free, as in not requiring parental fees. It was a change the then education minister, Rab Butler, would describe in the House of Commons as characterised by “dignity”; but 75 years later, under cover of Brexit, this basic pillar of our postwar order is being quietly eroded, with “free” schools asking parents if they can make a contribution to help meet the chronic funding shortfall they are facing. Money for the “little extras”, as the chancellor, Philip Hammond, in his recent budget, described the luxuries our pampered snowflakes enjoy these days – things like toilet paper, textbooks and stationery.

The penny dropped for me when I realised just how much schools are depending on these parental contributions. A Guardian report last month found that 43% of parents have been asked to make them, up from 37% two years ago. Their proliferation is hard to ignore.

And now the tone is beginning to change. The polite requests have, in some cases, morphed into the firm instructions more commonly associated with debt collection. One letter I’ve seen demands parents make a payment of £12.50 a month for each pupil, or a one-off payment of £150 a year. Bold and underlined type are employed to emphasise the point. A failure to respond prompts a follow-up failure to pay letter. The request is justified by the assertion that other schools demand £50 a month, so this is in fact a bargain.

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Here’s a conundrum. How does a school that struggles to pay for textbooks meet the increasing pressure to demonstrate high performance? Ofsted, the schools regulator, acknowledged last month that schools were limiting their curriculum to focus on end-of-year tests. A primary school teaching assistant I spoke to recently told me about children learning nothing but maths and English in their final year. The children who had no hope of passing were siphoned off into a dud class so that the higher performers could get on with providing the school’s required performance data uninhibited.

It has long been predicted that a two-tier system like this within schools would be disastrous. As the sociologist Michael Young, who coined the term meritocracy, wrote in 1958, children who have “been labelled ‘dunce’ repeatedly … cannot any longer pretend; their image of themselves is more nearly a true, unflattering reflection”.

Young – himself the project of a utopian school experiment that gave him a privileged education for free – remained prophetic until the end, lamenting not long before his death in 2002 that with “an amazing battery of certificates and degrees at its disposal, education has put its seal of approval on a minority, and its seal of disapproval on the many who fail to shine from the time they are relegated to the bottom streams at the age of seven or before”.

We argue endlessly about grammar schools, which back in 1944 were about focusing a superlative academic experience on those perceived to be more able. But the desperate financial situation facing comprehensive schools has made this intellectual segregation a reality. A school that cannot afford loo roll is not going to be able to offer stimulating outings and cultural experiences to all.

Some schools are overtly creating a top tier, where the most academic pupils are groomed for high grades and Russell Group university admissions, and offered experiences – such as residential and theatre trips – that are simply not available to the rest. One state school organised a £3,000 trip to Borneo, for those who could afford to pay – achieving class segregation through seemingly voluntary exclusion.

I doubt any of these trips are on the level of Eton’s, some of whose pupils went off to meet President Putin on a red carpet trip to the Kremlin. The gap between state school pupils and those at the most elite private schools – we in Britain have the biggest such gap of any country in the world – blasts all other inequality out of the water.

But we’d be wrong to assume that something akin to a level playing field exists in the state sector. Here too, children are effectively being segregated by class, and parents are now being asked to contribute, albeit on a smaller scale, for something that the 1944 act established as free. We may have moved a long way since Butler said the purpose of the modern school system was to bring “the fruit of modern knowledge, to aid the ancient skill of farm and field”. But in some ways, we are already going backwards.

• Afua Hirsch is a Guardian columnist

• This article was amended on 28 November 2018 because an earlier version referred to Britain “facing the horror of Stalingrad”. This has been corrected.