A plate of bulb-shaped courgette fritters filled with Manouri cheese – a light sheep's or goat's cheese, similar to feta but less sharp – with a salad of assorted leaves and pungent fennel tips, is an unusual way to start the day.

Yet it is a glorious one. Green vegetables, cheese, salad; none of these seems at all breakfasty, but fritters are served at this hour all over the Middle East and South Asia. As it happens, this dish from Yotam Ottolenghi's London restaurant Nopi is a delicious morning treat. Most of us, though, would never even think to order it.

It is curious that we British are so proud of our breakfasts and brunches. The Full English is a national emblem and, if you want to get fancy, order Eggs Benedict or scrambled eggs with smoked salmon after 11am, and call it brunch. But our morning consumption has not evolved and still lacks that va va voom.

Where we're going wrong, points out restaurateur Russell Norman, is that we ignore the "lunch" aspect of brunch. "Brunch in the UK doesn't mean people skip breakfast, they just have breakfast – usually eggs – for lunch instead. But in NYC, a truly 24-hour city, they appreciate the "lunch" part."

Norman is just one of those introducing New York's more mature brunching ways to these shores. Take the rest of Nopi's offerings: black rice and coconut milk with banana and mango is an exotic twist on a bowl of porridge and makes perfect sense in the morning. Who here would be brave enough to serve rice (other than in the form of Rice Krispies) for breakfast? Then there is the North African dish shakshuka, a blend of soft red peppers and tomatoes, chilli, coriander and eggs, baked together. This has all the hallmarks of a fantastic brunch.

"We still have a lot to learn from the Australians and the Americans," says Ottolenghi. "I can't think of many things I wouldn't have for brunch. It can, and should, include salads, savoury pastries, fish, spreads – anything, really. But Brits are very business-like. They find it difficult to relax in the morning. They want to get on with the day, hence have less time and patience to engage with food in the morning."

This is a shame, especially when Ottolenghi describes nasi lemak – a Malaysian dish of coconut rice with fresh cucumber, peanuts, dried anchovies and chilli sauce, meant to set you up for the rest of the day. The American diner-style menu at Spuntino has very different origins. Russell Norman heads up four London restaurants, with the others serving Italian food, although all are run along the New York brunching, diner-style ethos: the idea you can drop by at any time of day for any sort of food.

"There are only a few places in London doing brunch and breakfast well, such as The Wolseley," he says. "We serve an all-day menu from 11am. London is six to 10 years behind New York in terms of restaurants. We're catching up, but the problem is that here restaurants came from hotels, and in New York they developed from diners."

So confused are Norman's customers about brunch that he has taken the "brunch" section off the menu, and mixed it in with the other food to encourage people to order whatever they want. The style as well as the substance of New York eating has made Norman a devotee. There are no reservations, you eat at the bar and can indulge in free filter-coffee refills. There's plenty on the menu that is instantly recognisable to the average Brit, but there are novelties too. Sliders – which originated as a meatball between bread and are now any sort of mini burger – come in spiced mackerel, ground beef and bone marrow, lamb, and salt beef. They are damn fine. Grits come from the American South. They're a polenta-like starchy corn dish, served soft like porridge and come with a spicy sausage stew.

It isn't all fried, heart attack-inducing food. There are salads and some seafood dishes. But the show-stopper is a truffled egg toast, a doorstop of white bread with its middle scooped out to hold two eggs, covered in a thick layer of fontina cheese and spiked with drops of truffle oil. The truffle hits the back of the throat and then you settle into the comforting hangover cure of egg, soft bread and melted cheese. If you really are hungover, you might add a Bloody Mary to your order. That's one thing that differentiates us from US brunching: we're more than happy to get stuck into the booze during the day.

British chef April Bloomfield took the gastropub concept to New York with The Spotted Pig and opened the Breslin Bar & Dining Room. And she took on the brunch concept as well. "The equivalent to New York brunch is our Sunday roast, where pubs open at 11am and people meet their friends and family to have their roasts – it's exciting that brunch is taking off," she says.

New Zealander Peter Gordon opened Kopapa in London in 2010 as both a stylish all-day café and a smart restaurant. Head there in the morning and your idea of breakfast will change for ever. There are fritters, a chorizo hash and rocket with a fried egg and salsa verde, and Turkish eggs served with whipped yoghurt and hot chilli butter. And at the weekend, those brunch offerings are glammed up.

Some Brits are also working on the brunch conundrum. Bill Collison, founder of Bill's Café, has pimped the full fry-up by adding hummus, guacamole and sweet chilli sauce. At Made in Camden, the restaurant at The Roundhouse music venue, the weekend brunch menu reaches from grilled sardines on toast with harissa aioli and coriander to fried egg with sweet spiced chickpeas, labneh and pangrattato.

One explanation for why New York is the birthplace of the brunch is that it was a Jewish alternative to church on a Sunday, where a leisurely morning meal at home was adopted by restaurants. In Britain, we have the phrase "breakfast like a king", but we struggle to take our own advice. Eggs are a fantastic and easily adapted food but would a king settle for a plate of eggs in the morning? No: when he spotted what was adorning tables across the world, he would order up shakshuka, nasi lemak, courgette fritters, sardines on toast and a selection of sliders. Then he'd sit back for the morning and enjoy the feast with friends and a jug of Bloody Mary. Time we did the same.

More breakfasts from around the world

Egypt – ful medames and aish beladi make up a traditional Egyptian breakfast: slow-cooked fava beans dressed in lemon juice, olive oil and garlic, with a kind of pitta bread made with wholewheat flour and bran.

Turkey – sit down to a spread of fresh bread, feta and kasar cheese, tomatoes, cucumbers, olives, salami and other cured meats, and boiled eggs.

India – uttapam, pancakes made from fermented lentil and rice flour, are morning staples across southern India, and might be served with curries and chutneys.

Japan – fermented fish is a common part of a Japanese breakfast, along with steamed rice, miso soup, fermented soy beans, seaweed and pickles.

China – in the north, bao zi, stuffed steamed buns, are popular; in the south, congee, a rice porridge, could be served with sliced beef, pork, liver, kidney or thousand-year eggs (preserved duck eggs).

Pakistan – halva puri cholay, a combination of halva, made from semolina, and a chickpea and potato curry called aloo cholay, eaten with the deep-fried flatbreads, puri.

Mexico – huevos rancheros are the classic Mexican breakfast: fried eggs on a tortilla topped with a red tomato and chilli sauce. The dish is usually baked with some cheese and served with refried beans.

Burma – si damin is a variation on popular sticky rice (kao hnyin). Glutinous rice is boiled with turmeric, then fried on top of onion and garlic into a crispy rice cake. It is served with sesame seeds, dried shrimp and peanut.