I'm reliably informed that people visit Buenos Aires for reasons other than tango. Granted, it's quite a city, full of crumbling grandeur – and the resting place of one rather famous First Lady. But to me, as one of the more recent members of the international tango tribe, and to many others, the Argentinian capital is simply where a most extraordinary dance-form was born. And as such, it's the Mecca for any tango-minded European. In fact, you're not a dancer till you've spent some time here. Two weeks is a nanosecond – and won't qualify me for any tango street cred – but at least I got my first taster.

I visited at the beginning of July – wintertime in South America – and on Argentinian Independence Day was treated to the first snow the city had seen in 100 years. No one had mentioned before going that the pollution is at lung-mincing levels, but when I got back sporting my brand new Buenos Aires Cough, everyone nodded knowingly. How foreigners cope at peak tango time – February to March – when the non-stop festivals and the sweltering 40-degree heat kick in, I've no idea.

To clear up a common misperception, Argentine Tango – even more so the nuevo style that recent generations have developed – wouldn't be seen dead in the arms of Ballroom Tango (the stuff you see on the likes of Strictly Come Dancing). The real thing is improvised, requires no sequins or fixed grins, and is danced by everyone from cool young bailarínes to graceful old hands. It may look like the vertical expression of a horizontal desire, and undoubtedly there are a few who treat it as such, but the degree of concentration required means that sex is pretty much the last thing on dancers' minds.

I'd been learning for eight months prior to my trip – a toddler in tango terms – and stepping into the scene was one baptism of fire after another. I'd be counting stiletto wounds at the end of off-nights. But when it worked ... well, words just don't come close.

Milongas (tango venues) are wonderful places to while away an evening – or entire night – whether or not you're a dancer. Many of the traditional ones take place in old dance halls with oodles of atmosphere (the classic is La Ideal, immortalised in Sally Potter's film, The Tango Lesson), the trendier ones, like La Viruta, are packed to the gills with stylish young things; waiters supply a steady stream of alcohol and coffee, empanadas (mini pasties) and medialunas (mini croissants); and the scene is abuzz with activity – couples wordlessly coming together (eye contact is often enough to establish a connection), dancing together for several songs, then often wordlessly parting ways again. And the music, all aching bandoneons and doleful singers, seeps into your very bones.

If you want to learn from scratch, there are various schools (like the popular DNI Tango) that will take you under their wing. But once you've sussed out the scene, the best way to progress is one-on-one, with a respected teacher. Also, learning on the job, jumping in at the deep end at the nightly milongas and practicas (where the nuevo crowd gather to try out new moves).

Sightseeing occurred late in the day, after lengthy lie-ins. The famous Café Tortoni on the equally famous Avenida de Mayo lived up to all expectations – and exceeded in the case of their absurdly tasty hot chocolate. La Boca is sadly the Piccadilly Circus of Buenos Aires. San Telmo, though, is a gem – a bustling antiques market nestled in a beautiful central square. Looking down onto the scene from El Balcón, a tourist-trap café, but a pleasant one nonetheless, I spotted a middle-aged woman, shopping bag in the crook of her arm, dancing some kind of approximation of tango – solo. So that's how they go mad round here, then.

For the majority of my visit, I stayed in a nondescript but neat little apartment in the Palermo district. It had views of the city skyline and was in bus-ing distance of the main tango venues – plus, I could pretend I was a local this way. Then, for a couple of nights, I sampled the rather more sumptuous Kempinski Hotel in the chichi (but somewhat soulless) Recoleta district. I say nights, but in truth that's the one time of day the hotel and I didn't come into contact. The bed was huge and comfy – a detail you notice when you've danced your feet to blisters. Talking of feet, the Mecca within Mecca – for female visitors at least – is Comme il Faut, purveyor of tango shoes so outrageously gorgeous and inexplicably comfortable that even this former tomboy has caught the bug.

They were my most expensive purchase in a city which enables your pound to go a very long way indeed. Middle-of-the-night taxis only set you a back a couple of quid – though the taxistas try their best to fleece you, giving unrequested tours of the city as soon as they clock your out-of-town status. There's an edginess to Buenos Aires in general, a sense that you can't readily trust anyone. A friend – a local – had his wallet stolen and I was almost pickpocketed on the Subte (underground). But that's more to alert than to deter you – it's too unique a city to let a little argy-bargy put you off. And anyway, once you've been tangoed, there'll be no holding back.

Kuoni Travel (www.kuoni.co.uk; 01306 747008) offers a 5-night deal at the Kempinski Hotel in a deluxe room on a b&b basis, with BA flights from Heathrow plus transfers, from £1,300 per person