The idea, announced by the Prime Minister last week, of exhausted new mothers and fathers receiving parenting advice via text message is intriguing. It's a shame the texts won't be written personally by David Cameron, because I imagine they would read: "OMG is your baby not sleeping through yet?" or "Call that a middle name? LOL."

There will also be parenting classes, which can be bought with £100 vouchers handed out for free at Boots, and advice telling mums and dads to "keep calm during labour". LOL, indeed.

It is a pity that the coalition government will not ring-fence Sure Start centres, which are already giving out parenting advice across the country, from closure. But, we are told, Sure Start centres are not used by the people who "need them most" and have been simply hijacked by middle-class mummies who fancy a bit of free fruit and yoga.

Yet is this idea of "hijacking" resources a myth? When my daughter was nine weeks old, I turned up for my free fruit and yoga at my local Sure Start centre in Peckham, south London, expecting to see a queue of Bugaboo-driving yummy mummies outside. But at my weekly baby massage group this was not the case: we were from a range of backgrounds. And I was probably one of the most clueless in the room.

Because here is the second myth: that middle-class mothers and fathers automatically make the best parents. When we talk about "those who need it most", who do we mean?

Yes, it is just a handful of families, as Tony Blair first identified, causing the majority of anti-social behaviour in any one neighbourhood. But besides that core of "feckless" parents, what about the rest of us? At the time, my daughter was not sleeping, barely feeding. The Sure Start centre was invaluable.

The midwife there gave us advice about language development, and handed out free children's books. I smugly thought I'd be top of the class for already building up a library, but then she told us we shouldn't have the TV on when talking to our babies, even at this young age, because it might affect their speech later on. I was struck by guilt, because earlier that day I'd been entertaining my daughter on her playmat while a particularly juicy re-run of Dynasty boomed out in the background.

A health visitor told me that she believed many older mothers in the middle of their careers found it difficult to cope after having a child because they were used to being in control, and were suddenly confronted by a messy house and the unpredictability of a baby.

In her view, working-class, younger mothers coped better because they were used to life dictating to them, not the other way round. The working-class parents were more likely to have their own mothers living near by, while the university graduate was more likely to live in a different city from hers. So support networks were better, the health visitor said.

This was her experience, but is it true? It would be better to avoid generalisations altogether, and we must not assume that the middle classes make good parents just because they can afford the nicest clothes and toys. But many can pay the £200 or so for the antenatal classes offered by the National Childbirth Trust, for example, which, crucially, put parents-to-be in touch with a ready-made support network of new mothers – a huge advantage over parents who cannot afford the NCT classes.

Sensible, calm parenting should not come at a prohibitive price. The benefits of networks such as the NCT's perhaps show that there is a need for what Mr Cameron called a "sensible state" to offer help, for free, to parents who want it. But, please, Prime Minister, protect our Sure Start centres, too. And maybe go easy on texts telling us to "keep calm during labour".