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This zingy palette was set way back last autumn at the international fashion shows, where the big design houses embraced art and, with it, rainbow brights. At Chanel – which seems to become younger in spirit as its creative director, Karl Lagerfeld, gets older – suits and dresses in tweeds made up of tiny squares of vivid colour, like those in a paintbox, were shown in a make-believe contemporary art gallery amid pieces of sculpture. At Prada, huge, vibrantly smeared painted portraits lined the catwalk and were replicated on dresses. At Dior, Raf Simons went for bold reds and yellows in his collection.

Such statements from the big houses don't always translate into people actually wearing them. But after a particularly wet, grey-skied winter and sudden sunshine over the recent holiday weekends, it seemed that customers were ready for a pop of bright colour – demanding it, in fact.

Last month, when I met Lesley Torson, the owner and head buyer of Trilogy, a London chain of designer-denim boutiques, she'd put in urgent orders for bright pink items due to customer demand. They haven't stopped selling. "Pink has even outsold white for the first time ever," she says. "We've reordered our key pink styles from J Brand and Current/Elliott five times already this season. When the sun comes out, everyone feels more adventurous."

Rosanna Falconer, head of digital at Matthew Williamson – a British designer who, inspired by the vibrancy of India, Ibiza and Morocco, has been bringing bright colour to these shores since the late Nineties – has noticed a growing confidence among women. "They're learning how colour can alter your mood and outlook, and that of people around you. As Matthew says: 'Colour can be just as powerful as black; be the girl in the pink dress in a sea of black.'"

Other influential London fashion designers, such as Jonathan Saunders and Roksanda Ilincic, have made bright colour a signature and shown that it can work for women in their thirties and beyond. Ilincic, whose first store opens in Mayfair this week, and whose current collection includes mid-length skirts in bright yellow, puts her love of an eye-popping tone down to her Balkan roots.

"The colours in Serbia are so bright," she has said. "We're all more optimistic when the sun is out, and I thought that happiness could be transported to others in a dress. It's so important my designs feel uplifting. If you are happy, everything you wear looks better."

Ilincic, a stunning beauty with a porcelain-white skin tone, wears the fuchsia-pink and sunset-orange pieces she creates – and always with a bright lipstick. This has helped to educate her customers (which include Samantha Cameron, Michelle Obama and Julianne Moore) how to wear brights.

Falconer says the rising popularity of separates over recent seasons has rendered brights more wearable for those who might have been previously fearful. "An orange pencil-skirt or scarlet palazzo pant paired with a simple white T-shirt is a far less daunting prospect for a woman emerging from a winter in muted tones," she says.

Bennett at John Lewis says: "Part of the reason for its success is that the brights trend is extremely versatile. Don't be afraid to dress all in colour – it can be surprisingly flattering. If this is too much for you, try a bright top and darker trousers."

Something about bright colour and black jars for me, but navy trousers or a jacket paired with fuchsia, purple, orange and emerald green looks rich and considered. Lupe Puerta, global head of personal shopping at Net-a-Porter, says: "Most people gravitate towards black, but I'd recommend teaming brights with tan, grey and white instead, as it softens the look and feels much more relevant for summer."

Everyone I spoke to agreed that the easiest way to buy into the trend is with a bright accessory. For Puerta, it's the British shoe designer Sophia Webster's playful kaleidoscopic heels or Bottega Veneta's signature leather shoulder bag updated in bright pink. I like Matthew Williamson's raffia-embellished flats in lime and cherry-pink. Whistles's mint green medium clutch for £55 can't be argued with, either.

With everyone gearing up for the World Cup in Brazil – the land of festive colour – this summer is only going to get brighter. The weather may not play nicely, but that's even more reason to give our wardrobes a colour boost.