It was way past lunchtime, every restaurant I’d walked into in the past half-hour was full of people blatantly eating and drinking and enjoying themselves, every one of them mocking me for being the only person in Buenos Aires who wasn’t being fed, and I was dizzyingly, cripplingly, chewing-on-my-own-tongue hungry.

I had ended up outside Los Gauchos, one of the city’s many parrillas – Argentine institutions where chefs sweat over a mammoth grill cooking steaks, sausages and little else. Not great for veggies, parrillas.

There’s one on almost every corner, some posh, some not. This one was not. It was small and shabby and, again, packed, but a couple right in front of me were just paying their bill.

Ignoring the fact that I could count four kinds of stain on the shirt of the fat old waiter, I sat down. There was no tablecloth, no condiments, no cutlery.

The waiter turned to me and said “What do you want?” in Spanish. Which is when I noticed that there was no menu. I asked what he recommended – basically meat, I didn’t really catch exactly what – and ordered that. Which was when I noticed that nobody was speaking English, because, gloriously, nobody was English. This was a locals-only diner, serving great red mounds of meat and spaghetti on small, white ceramic plates.

The waiter returned with a bottle of lager, a breadbasket and a cockroach. I devoured a piece of bread. So did the cockroach. I didn’t see him at first, as he was slightly smaller than his meal, but when I tried to take the bit of crust he was eating, there he was. Rather than scuttling off in fright, he merely sat on his prize and gave me a look.

I did think of complaining, or even leaving. I did. But I really was hungry. So I just took another piece of bread.

Which is when the waiter came back with my lunch. Turns out I had ordered topside of beef, which, interestingly, had been roasted, not grilled. I got two steaks – long slabs of pinkish meat, with thick, creamy lines of fat on one side – and little crispy roast potatoes cooked in tomatoes, garlic, onions and herbs, all covered in thick, dark gravy.

It was ridiculously good. The steak was sensational, as tender as a teenage heart, and the roast spuds that had soaked up the gravy were so perfect, I temporarily forgot about the steak. I certainly forgot about the cockroach, and, after the initial, ravenous, disbelieving mouthfuls, I ate slowly and deliberately. A plate of that, and a beer, cost £3. I’ve paid 10 times that in London and not eaten as well.

If you’re ever anywhere near Buenos Aires, make a pilgrimage to Los Gauchos. Ask the fat waiter in the stained shirt what he recommends. And don’t worry about the cockroach. You get enough bread to share.

Los Gauchos, 372 Chile, Buenos Aires

Travel brief: the only direct flights between the UK and Buenos Aires are operated by British Airways (0870 850 9850, www.ba.com), from Heathrow; from £792. The city’s grandest hotel, the elegant Alvear Palace (00 54 11-4804 7777, www.alvearpalace.com), has doubles from £234. More modestly priced is the stylish Hotel Trebica (4372 5444, www.hoteltrebica.com.ar ), with doubles from £55. Alternatively, you can rent an apartment from as little as £10 a night. Try www.stayinbuenosaires.com.ar.

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