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At Apple's London HQ just off Regent Street, two executives have flown in from San Francisco to deliver an iPad Air 2 briefing. We gather in a small meeting room along with a magazine writer, dressed neatly in a shirt and well-polished brogues. I imagine they are Grenson or Church’s. I am in fluorescent orange Adidas trainers and matching luminous running jacket, sports bra, yoga leggings. A Bern helmet dangling from the straps of my shoulder bag (which is actually a pannier) nearly swipes an iPad clean off the coffee table. I apologise. My bike is parked outside and I have turned up to a meeting in my cycling gear.

Of course, nobody bats an eyelid. This can’t be the first time everyone here has had a meeting with a slightly perspiring Londoner in sportswear (tech companies, after all, are not fussy about ironed shirts and suits). And, as far as I am concerned, cycling kit now qualifies as appropriate business attire.

There are a few basic guidelines of course: quick coffee with a contact — trainers and reflectives come as standard; after work networking event — change the shoes into something less obviously sporty; important one-to-one with a top boss at a key company — choose the most muted colour cycling tights and throw a shirt on over the sports bra after locking the bike to a lamppost. But most of all: don’t let work get in the way of a bike ride.

Plenty of London’s cycling commuters are dressing for business success in cycling gear, too.

“I often tip up at meetings on the bike,” explains Timothy Ryan, an adviser to and investor in media businesses and start-ups.

“I’m lucky that I’m in the creative/media industry so I can get away with it more easily than many others, but with the rise in cycling across the board, it’s far more acceptable than it was a few years ago... More than anything it’s a great ice-breaker.”

Like me, Ryan varies his gear depending on whom he is meeting. “There are two versions of ‘bike me’ at meetings,” he explains. “With cyclist clients, they’re cool with full MAMIL [middle aged men in Lycra] cycling kit and usually want to compare ride notes and ogle bikes before the meetings. With non-cycling clients I’ll usually be in cycling-friendly jeans and a shirt and they may be a little bemused by a perspiring brow.”

Admittedly, some are still more than a “little bemused” by those of us who like to shake hands with a suit in a fingerless mitt.

Emily Brooke, founder of Blaze, a pioneering cycling product start-up, cycles everywhere. “I bike to meetings with lawyers, investors, agencies, partners and I wear Lycra because it’s what I’m comfortable in and it’s practical. Everyone on our team bikes daily so why shouldn’t our attire reflect that?”

Yet there are perils with this and she has had a couple of run-ins — once in the early stages of her business.

“I was working with fancy intellectual property lawyers in High Holborn. I’d arrive at their offices, often late, and somehow always through a rain storm, clad in helmet and Lycra. The office secretary would always look me up and down with an ‘Oh she’s here again’ face,” explains Brooke.

“One day I arrived thoroughly soaked and with just about enough time to nip into the bathroom and change my wet leggings for a dry pair — wishing not to leave a damp puddle on the chair after my meeting. I didn’t want to take a sopping wet pair of leggings and underwear into the meeting room with me, so left them in a little bundle under the sink to collect on my way out.

“Unfortunately, the secretary got to them first and as I was leaving and shaking hands with the men I had just met — one the owner of the firm — she proudly came up brandishing my soggy garments.”

Another guideline, then: always carry a spare pair of pants and a wet kit bag. Yet self-righteous women are perhaps less of a worry than creepy men.

Recently at a meeting with a fellow start-up founder she had never met before, Brooke received a disturbing email from him that suggested her “yoga pants” had left him in a sweat. It led her to wonder for the first time “whether it’s partly my fault and whether I should be in Lycra in the office”, she says.

Simon Mottram, founder of Rapha cycle clothing brand, may have the answer. “I have worn cycling-specific gear all day, every day for the last 15 years,” he explains. “Initially as a consultant I found that clients would accept that this is just the way I dress. Now, at Rapha, our dress code is relaxed and we all wear a mixture of regular clothes and Rapha/cycling clothes. But they don’t have to look like cycling clothes to work on the bike.” Here’s where Brooke might get interested.

“As more and more Londoners have turned away from their cars or the congested public transport in favour of the bike, so the way we dress needs to change accordingly. We need clothes that work well on and off the bike — that allow us to move seamlessly between different modes and environments,” he says. “The fabrics don’t have to be technical-looking — they can be beautiful, using merino and other natural fabrics and hybrids.”

So no more Lycra? “The traditional cyclist was often prepared to pull on some old sweatpants and a DayGlo jacket to ride to work. I never understood this — why do people think that they’re invisible for an hour a day on their commute?” says Mottram. “Yes, for many of us execs, cycling clothing is increasingly acceptable in all but the most stuffy work environments, but the cycling clothing doesn’t have to look like it’s for cycling. Indeed it can sometimes look even better than the best non-cycling alternatives.”

So meet me at noon — I’ll be the one in (attractive) reflectives.