It's that time of year again – my partner and I are locked in the Squash Wars. The opening salvo is fired towards the middle of October, when I cheerfully suggest ordering the seasonal squash box with our organic veg delivery, and am met with a firm refusal from my pumpkin-hating other half. I then spend the rest of autumn trying to persuade him of their healthful deliciousness, while sneakily stocking up on squash at the supermarket.

If you're not a squash-lover, this is a tough time of year. Every greengrocer has piled-up displays of gourds of all colours, shapes and sizes, from grapefruit-sized gem squash to giant hundredweights and hubbards (the largest pumpkin ever grown weighed a whopping 922kg). They are all members of the cucurbita family, which also includes melons and cucumbers. Although the terms "squash", "pumpkin" and "gourd" can be used interchangeably, "pumpkin" generally refers to the large orange varieties carved for last week's Halloween lanterns, "gourd" to the oddly shaped, nubbly skinned decorative fruits, and "squash" to all the other edible varieties.

British consumers are becoming increasingly enthusiastic about squash, says Rachel Lovell of Riverford. In 2011, the company sold about 4,500 of its mixed squash boxes; last year the figure was up to 6,000, and the trajectory appears to be continuing this year. But if your exposure to squash is limited to pumpkins, you may be disappointed – cultivated for their bright colour, even shape and easily carved skin, these can be lacking in the taste department.

"Pumpkins have a higher water content and a less dense flesh. This means they are not as flavoursome, but with the right cooking, can still make a tasty dish," says Lovell. "Add plenty of flavour and spice – for soup use good stock and perhaps lentils to give the texture a boost, or try a Thai curry."

Anna Hansen, chef at The Modern Pantry in Clerkenwell, London, agrees that Asian flavours make squash sing. "The sweetness of squash is fantastic with miso, tamarind and chilli," she says. "I love a chilli-roast squash, pancetta and miso soup, or tamarind-roast squash, feta, toasted pumpkin seed, red onion and grilled radicchio salad. I find roasting yields the best flavour, as the combination of moisture evaporating and the natural sugars caramelising intensifies the flavour."

Yotam Ottolenghi takes this flavour-concentration approach a step further. "I like to sear slices of squash on a hot griddle pan before they go in the oven for about five minutes, turning once, so that both sides get nice charred lines. This intensifies the flavour in a wonderful way. Squash is so versatile that it can go all ways: creamy, spicy, sweet, crunchy or smooth," he says.

Sought-after spaghetti squash. Photograph: Alamy

Of the hundred or more squash varieties available, from acorn to zucchini, perhaps the most elusive is the spaghetti squash. As its name suggests, the fibrous texture of this gourd makes it an acceptable low-calorie substitute for pasta, and followers of low-carb and fasting diets have hailed it as a miracle ingredient.

It is rumoured that the scarcity and high nutritional value of spaghetti squash has led to an underground market in the fruit, with dieters swapping sources online – but only once they've secured their own supply. I asked Adrian Browne of The Creaky Shed greengrocer in Greenwich, south-east London, if there is any truth to this. "We sell them when we can, but they're certainly really hard to get hold of," he says.

"All our squash is grown in Kent, and our supplier has had no spaghetti squash this year. Every day we have customers wanting to know whether we'll be getting them in. People are using more pumpkins generally, and spaghetti squash is a new fad … The growers haven't caught up with demand." In fact, growing your own may be the way forward – they are relatively easy to grow from seed.

"They have mythical status among low-GI dieters," a carb-conscious friend says. "I've never been able to find one in a mainstream shop. Personally, I prefer julienned courgettes as a lower-carb pasta substitute. Not that I'm bitter or anything."