They're cheap and tasty but low on guilt, says Simon Usborne.

When Cloudy With A Chance of Meatballs was released in Israel, the title of the 2009 animated comedy, set in a town where food falls from the sky, was adjusted to feature a more familiar dish. Now Geshem shel Falafel, or "rain of falafel", could be a gastronomic forecast for Britain as we develop a growing appetite for the politically contested fritters.

A chickpea downpour is moving west towards London and beyond as Just Falafel, a fast-food chain founded in Abu Dhabi six years ago, prepares to open 200 branches across the country in the next five years. It already has three in the capital, with a fourth soon to open along with outlets in cities such as Cambridge and Exeter.

The traditional falafel map encompasses much of the Middle East, as well as Sudan and Egypt, where traces of fava beans are evident in the tombs of pharaohs. Wraps are also a staple in New York, the world's foodhall, thanks to the influences of the city's Israeli population. But Britain has been largely starved of the dish, reserving it for Middle-Eastern cafés, festivals or the pages of vegetarian cookbooks.

At the Monmouth Street branch of Just Falafel in Covent Garden, a queue winds out on to the street as Bilal from Lebanon fries balls of mashed chickpea and fava beans bound with onions, garlic and coriander. He then rolls the falafel in flatbread with pickled cucumbers, pickled turnip, parsley, mint and tomato, finishing the wrap with a tahini sauce made of ground sesame seeds.

Recipes vary according to region and the whims of mothers, and are disputed along borders, most notably that between Palestine and Israel. Whatever the precise ingredients, and ratio of chickpea to fava, the best falafel wraps combine the comforting, herby crumbliness of the beans with the sharpness of pickles, zingy freshness of the tahini and a hint of spice.

Patrick Matthews is a long-time falafel fanatic enjoying the growing demand for fried pulses. He discovered the delicacy in Damascus, where he was studying Arabic while at university in the early 1970s. "I'm pretty sure I'd never even heard of falafel before then," he says. Later, he adds, "I associated it in the UK, like cannabis, with music festivals and vegans".

After a career as a writer and journalist, Matthews, now 59, decided to bring falafel to a new audience – and make healthy, Middle-Eastern food more appetising. In 2004, he remortgaged his house and recruited some Sudanese friends to sell falafel wraps from a van in Hoxton Square, east London. Deckchairs beside the van suggested the seaside, so Matthews named his outfit Hoxton Beach.

His own fledgling falafel empire now includes four London branches, though he doesn't have expansion plans as ambitious as Just Falafel's. On a busy Saturday lunchtime on Ropewalk, a Diagon Alley of street food against railway arches in Bermondsey, south-east London, Rasheed loads the mix into a scoop, dispensing the balls into the fryer in one, blink-and-miss motion.

The Hoxton Beach wrap, a labour of love perfected over a decade and loaded with pickles and tahina, is thing of wonder. And it more than holds it own alongside the carnivorous competition. "We went to a beer festival recently and I always thought people drinking beer wanted animal protein," Matthews says. "I was surprised [that] we were almost the main destination."

Hoxton Beach and Just Falafel were among the beneficiaries of horse burgers ("if you run a vegan food business you can count on a meat-related scandal every few years," Matthews says) but the delicacy's rise is about more than a backlash. Chefs such as Yotam Ottolenghi, from Israel, have boosted appetites in Britain for Middle-Eastern cuisine. Hummus sales have soared in the past decade, while pre-packed falafel has become an everyday item in supermarkets.

Wraps, meanwhile, as New Yorkers have known for decades, are the perfect fast food, combining the warm, savoury satisfaction and convenience of, say, a burger, without, perhaps, the same amount of food guilt. Just Falafel is upfront about its fast-food credentials. Meal deals include fries and a soft drink while wraps come in enough varieties to make McDonald's look uniform. The "Japanese" includes wasabi mayonnaise and ginger dressing, while the American comes in burger form. Each wrap contains about 500 calories – the same as a Big Mac. But, the company says, these are "good" calories high in protein and low in saturated fat.

Fadi Malas is Just Falafel's chief executive, based in Dubai. He wants falafel to be a staple of the Western high street and food court. "Even here in Dubai had we not opened my kids would have never heard of falafel," he says. "The idea of a falafel shop is small on the sidewalk in the least prominent retail environment. We're changing that position."

Malas is also part of a new generation of Middle-Eastern fast-food merchants trying to reverse the global flow of deep fat. Maoz, from Israel, and Bateel, from Saudi Arabia are two other brands getting a foothold in Europe after decades in which US fast-food giants have dominated their region.

But it's within the Middle East that food – and particularly falafel – can become divisive. When Barack Obama travelled to Israel in March he expected to cause controversy – but perhaps not because of his breakfast. Before his trip, Israeli media reported that President Shimon Peres planned to serve falafel, inflaming a simmering food war that mirrors the broader conflict in the region. Israel and Palestine are among those countries who claim falafel as their own. "The Israelis have stolen the land and even the culture, and now the cuisine," Mahdi Abdul Hadi, a Palestinian academic, told Gulf News before the Obama trip.

The row perhaps peaked a few years ago when postcards emerged showing an Israeli flag planted in falafel below the word's "Falafel – Israel's national snack". Palestinians responded by pasting their flag over Israel's. Elsewhere, a taste for falafel has helped to unite Jewish, Muslim and Christian communities, but this offended Islamic zealots in Baghdad. In 2006, they ordered falafel sellers to leave the streets, shooting dead two who refused.

The forecasted "rain of falafel" in Britain shows how, regardless of its disputed roots, the food is becoming an international cuisine. One dreads to think what a Palestinian falafel maker would make of the "quesadilla" option at Just Falafel.

As food wars continue to sizzle in the region, the cry of those who seek to placate falafel activists – and perhaps convince those still unsure about the merits of minced pulses – has always been: "give (chick) peas a chance".

Patrick Matthews' Falafels

Makes about 20

175g dried chickpeas (not boiled)
325g fuul (skinned and dried broad beans)
1 medium onion, chopped
4 cloves of garlic
The white part of a leek
3g white pepper
3g black pepper
6g ground coriander
4g ground cumin
4g ground allspice
Half a bunch each of chopped parsley and coriander
Bicarbonate of soda
Sesame seeds (optional)

Soak the chickpeas and beans, separately, for 24 hours. Then grind them with all the other ingredients apart from the bicarbonate and sesame in a food processor or meat mincer. You will now have a stiff paste. When you are ready to deep fry, ideally in groundnut oil, add some water, optional sesame seeds for decoration, and a teaspoon or so of sodium bicarbonate.

Roll the mixture by hand into squash-ball-sized lumps or use a specialised falafel scoop, and put them one by one into oil heated to 180 degrees celsius. Turn them with a slotted spoon and remove when golden to drain on kitchen paper.

If the mixture becomes too wet and doesn't adhere, add some flour or better chickpea flour (Besam). This is likely to be necessary if you haven't found fuul and are using just chickpeas. Do not drop the balls in the oil from a height, as the hot oil will splash you – roll them in from just above the surface. Keep trying if the first few don't come out right. Eat with turnip and cucumber pickles, flat bread and tahini.