Last weekend I travelled without my baby for the first time, and I needed to express milk ahead of my seven-hour flight to New York. A member of Heathrow staff told me I should use the baby changing room. I felt bad that I would be occupying the room for at least 20 minutes, but I also felt bad because I thought my breasts might otherwise explode, midway over the Atlantic.

It seems someone knocked (I didn’t hear them) and when they got fed up with waiting they sought help. I heard keys jangling, and then a male attendant unlocked the door from the outside. While my breasts were still exposed and stuck inside a plastic pump, he began lecturing me about how I should pump inside the terminal building or leave the room unlocked.

In my formal complaint to Heathrow, I explained that this is not dissimilar to someone bursting in on you while you are on the toilet and then, with your pants still round your ankles, accusing you of hogging the bathroom. But I also said the problem wasn’t really the attendant’s reaction, it’s the system.

No one has given any thought to breastfeeding women at the airport: we have no dedicated place to pump or nurse in private and the staff have no training in how to handle these issues with sensitivity.

In case you haven’t yet become acquainted with the ungainly contraption that is an electric breast pump, I’ll fill you in. It consists of a motor attached with tubing to two bottles topped with plastic cones that are designed to fit over your nipples and create a vacuum. With every electric suck, your nipples are gruesomely distorted and milk is forced out and into a set of bottles. The effect is so undignified and so evocative of industrial dairy farming that I prefer my husband not to see me use it – and it’s definitely not a piece of tech I’d like to whip out in the main terminal building, or in the airport Pret a Manger.

Every day, about 1,300 planes land and take off from Heathrow, which means there must be hundreds of breastfeeding women passing through. Not all of them will feel able to nurse or pump in public. If, as a result, they decide not to ahead of a long flight, they will not only feel painfully engorged, but they put themselves at risk of a potentially serious condition called mastitis. Surely it’s not too much to expect a couple of small cubicles, with a chair and a plug socket, to be provided?

But this isn’t just about Heathrow. The UK has the lowest breastfeeding rate in the world. According to one study conducted in 2014, boosting breastfeeding rates in this country could save the NHS up to £40m a year by reducing the incidence of certain childhood diseases and breast cancer. In the UK, 80% of women who stop breastfeeding within the first six weeks do so before they want to, which suggests a serious lack of medical and institutional support.

Creating places for us to breastfeed would be a step in the right direction. A survey by Public Health England found that a third of women feel uncomfortable or embarrassed to nurse outside the home. We tend to place the onus on women to fix this, by baring our breasts in public and loudly asserting our rights should anyone tell us to cover up. Why not instead give women the option to nurse or pump in private, without having to sit on a filthy toilet seat or hog a precious baby changing room to do it?

The US offers an interesting example, in this respect. Its breastfeeding rates are higher than the UK’s – even though it is one of only a few countries in the world that has no statutory maternity leave and many women are forced to return to work within weeks of giving birth. One positive side-effect of this terrible policy is that there’s far greater recognition of the needs of women who want to continue breastfeeding while also working full-time or travelling.

Employers with 50 or more employees are required by law to provide break times and dedicated private spaces for female employees to express milk. In the UK they have no such obligation. Nursing pods are also becoming more common at American airports.

The policymakers tutting over why only one in 200 British women breastfeed their babies for over a year do not seem to have noticed that they have left women with a difficult choice: stay tied to your baby 24/7, pump your milk while sitting on the loo – or move on to formula.

We can’t rely on goodwill alone to change things. Heathrow did not formally apologise until my story made news on both sides of the Atlantic. The airport has now said that it will look at whether it’s possible to create space for nursing women. That’s not exactly a commitment to change, but it’s a start – and a welcome acknowledgement that we deserve better.

• Sophie McBain is a contributing writer for New Statesman and is based in New York. She tweets @semcbain.