It's hard to imagine it now, but if you wanted to eat out in London in the 1950s, you didn't have a lot of choice. The culinary landscape, according to an article in Design magazine in 1966, "was a kind of visual and nutritional desert between the works canteen and the Ritz". Grubby cafés and fusty Michelin-star dining were doable; if you were an ordinary person who liked to eat well, though, you could forget about it.

Who changed this? Who started the culinary revolution that culminated in Jamie Oliver enthusing about a bad-ass custard tart? Well, Terence Conran was partly responsible. So, too, was Peter Boizot, who opened the first Pizza Express in 1965. But another, overlooked name deserves a mention: that of Reginald Wray Frank Eastwood, a butcher with big dreams and a passion for beef, and the man responsible for the existence of the (Aberdeen) Angus Steakhouse.

Dazzling modernity might not be an epithet that the casual visitor would associate with an Angus Steakhouse today. But when Reg Eastwood went in with Tom Beale, an accountant, and Peter Evans, a bar owner, to open up the first branch in Soho, they were doing something new. 'Supremely succulent Scotch steaks' at 'prices that won't spoil your appetite' was the proposition, the perfect meal to cap a big night out in the West End. The plush leather, the saucy crimson lighting, and above all the sophisticated food, prawn cocktail and Black Forest gateau and tons of red meat: this was fine dining for everyone. There were banquettes, for God's sake. Before long, the chain was thriving. It even got into the Good Food Guide.

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In one sense, everything has changed at the Angus Steakhouse. In another, nothing has at all. Whatever the official name, the signs still say 'Aberdeen'; the Camembert is still baked. And yet outside, London has transformed. In 2014, everyone is a gourmet, and the lucrative casual dining market is more hotly contested than ever. Fancy butchers are popping up all over town. Mention the continued existence of the Angus Steakhouse empire to anyone who lives in the capital and you will get the same disbelieving response: a snort of derision; the observation that you never see anyone actually eat there; and, if you reveal that you intend to, a look of the deepest sympathy.

Industry insiders feel the same. "They are such a total cliché, so outdated, and the quality just is not up to scratch, in a very competitive market," one tells me. "They have these great sites in iconic locations, and I would assume they'd get a better return if they sold up to Côte or Byron. You hear a lot of debate in the sector about how they manage to hang on." And yet, somehow, Reg Eastwood's dream survives. The question is: how?

As part of my efforts to figure that out, I went along earlier this month with Richard Turner, executive chef at Hawksmoor, a small chain that shares a favoured meat with Angus but very little else. Richard, a broad, energetic figure with the cheerful resignation of a man whose job involves eating steak every single day, has worked with such chefs as Marco Pierre White, Alain Ducasse, and Pierre Koffmann; he co-owns Turner & George, one of those posh butchers. He knows his meat. But he hasn't eaten here before. He wears an air of sceptical anticipation as we walk in.

The first thing you notice when you visit an Angus Steakhouse: the general perception among locals that they run on empty is wrong. In fact, there is a steady stream of punters. And this Friday lunchtime, the place is more or less full.

We're at the Coventry Street branch, one of three around Leicester Square. (The other three are also in central London; some have been given a modern makeover, some still look like particularly subdued strip joints.) Richard surveys the menu, and notes the second thing that strikes you about an Angus Steakhouse: the price. At £26 for 12oz of fillet, or £22 for a 10oz sirloin, they bear comparison with the significantly ritzier Hawksmoor, among other well-reviewed restaurants a short walk away; for that money, you don't even get sides thrown in. A three-course dinner for two with wine can easily go past £100. At Pizza Express, you might eat the equivalent for £30 less.

Luckily, The Independent Magazine is paying. Richard gets a ribeye with sides of mushrooms, mac and cheese, and chips. A waiter and a chef have told me that almost everything, apart from the steak, is pre-cooked and then warmed up on site; I've already eaten the chicken, and I believe them. So I ask for the smallest sirloin available, and leave it at that.

So. What's Richard hoping for? "The produce is everything, really," he says. "If you haven't started out with a good piece of beef – grass-reared, dry-aged – you're screwed." If the menu is to be believed, we should be in for a treat; on it a butcher called James Cambell explains that, "We are committed to the ethos of providing Angus with the best-quality meat sourced from animals who have grazed in open pastures". Wanting to explore this further with Mr Cambell, I ask to speak to him, but unfortunately no one at Angus's parent company is able to put me in touch, he has no internet presence that I can find, and when I call the chain's suppliers, Maren Meats, they tell me I must have the wrong number.

Then there's the cooking. "We cook it over charcoal, and we grill it very, very hot," Richard says of Hawksmoor's methods. He is a firm believer that the more of the steak exposed to the heat, the better it tastes. "We're always moving the steak," he says. "We want that colour all over it."

As he finishes explaining, our food arrives. Richard lets out a morbid chuckle. "Well, yours is terrible," he says. "Mine is better." He gestures to the stripes seared in neat lines across the sirloin, suggesting it hasn't been moved at all in its time on the grill. "You want to see a lot more of that. They haven't even bothered."

We tuck in. The mushrooms are good. Just as on my last visit, though, the sirloin seems to be unseasoned. Although identifiably steak, it also carries other, quite alien qualities: there's a fibrous density to the meat, almost like a pâté, and a headiness that I associate with game. The combination, topped with a creamy, flavourless sauce (from a packet, staff confirm) that has allegedly at some point been exposed to peppercorns, makes me think of decay: charity-shop coats, mulched leaves in a drainpipe. Also, I've asked for it rare, and it isn't. Richard leans over. "Cuts quite nicely," he says. He pops a bit in his mouth and chews.

He goes quiet. Frank Sinatra croons in the background. "That's... that's terrible meat," he mutters. "The margins they must be making." He shakes his head, and takes another small mouthful of his ribeye, and puts down his cutlery. "Let's go," he says abruptly. "Let's go to Hawksmoor. I didn't want to come here and slag it off, honestly. But I think this may actually be the worst steak I've ever eaten."

You may discount this whole stunt as the canny acumen of a direct competitor. I can't be so dismissive. I was there. I heard the note of dismay in his voice. I saw the haunted, faraway look in his eyes. And so we went to Hawksmoor, where I ate an excellent steak – that cost about 25 per cent less.

To all of this naysaying, the Angus Steakhouse has a robust answer. "Journalists occasionally try to say that we're dated and all that," says David Biesterfield, development director of parent company the Noble Organisation. (He may be thinking of the time that AA Gill observed that eating the restaurants' steak was "like eating old Enoch Powell speeches".) "Luckily, our punters disagree. The footfall and our continuing success show that up as the claptrap that it undoubtedly is."

Neutral observers agree, even if they put it a bit differently. "Canny Londoners might know where you can get far better food for less money, but not the tourists," says Simon Stenning, who runs consulting firm Allegra Strategies' food service division. "It's bright lights, big city, and you want something to hang on to that's familiar and trustworthy. They're easy to find, and you don't have to queue to get in. It's a bit exploitative, but it goes hand in hand with the location."

These insights are quite hard to back up with numbers. The Noble Organisation, a national leisure empire that also incorporates tanning salons and amusement arcades, is a family business, run by the eponymous Philip Noble. It is a firmly confidential company, with no PR department, and it doesn't share the restaurants' financial results. "We like it that way," says Biesterfield, who has proved quite hard to get hold of. "We prefer to let our products do the talking."

Still, those who work at the ground level are convinced that the business does well. "I've heard the Coventry Street branch does £350,000 a week," one waiter says. "There's a £1 cover charge – on one Saturday they can make £2,500 just from that." In a video posted on the Angus Steakhouse website, an executive chef called Martin offers his version of why the places are so successful. "The nice thing is, we're owned by one person, so we don't have to wait like normal companies," he enthuses. "We move with the times. We like to be dynamic, we like to be at the front."

The Noble Organisation has been at the front since 2002. In the end, Reg Eastwood's dream proved dispensable; in 1965, the business was sold to a chain of cafés called Golden Egg. In 1984, an entrepreneur called Ali Salih took over. Salih changed the banquettes from green to red, a step that proved bafflingly good for business; otherwise, his reign was a turbulent one, encompassing BSE, foot and mouth, and a high of 700,000 steaks a year, followed by a long decline. In early 2001, an ITV show called Restaurants From Hell found something unexpected in a vat of gravy: mouse droppings. "I have been doing this for 17 years and become fairly hardened," the inspector who made the discovery said, "but even I have never found mouse droppings in the gravy."

Whether you put it down to mad cows, mismanagement, or mouse shit, things weren't looking good. Salih was soon forced to put the business into administration; in 2003, just when it looked as if it was all over, Noble bought up eight of the 21 sites, feeling, I am told in a statement, "that the previous management had lost sight of the reasons why it had been so successful in the past". The restaurants have been refitted, the statement goes on, and the plan is to "continue to innovate in terms of our core products"; in general, though, the philosophy is: "if it's not bust, don't mend it".

While the empire might be smaller than in Salih's day, every one of the six outlets that remain has a brilliant location. Two property agents I speak to estimate that the Coventry Street lease would attract a premium of £2-3m. "To the best of our knowledge, they're not interested," one of them says mournfully. "Even if it's a very good offer."

Such premises, of course, mean that you get a very specific kind of customer: one who is unconcerned by the fact that the nearest landmarks are the Trocadero, Ripley's Believe It or Not! and M&M's World. "The people you get here are all tourists," says a waiter who I'll call Joe. "Even the British people who come here are visiting, but they know what they eat, and they know it's crap. If you complain, the manager takes it off the bill, he thinks the problem is solved, but you don't come back. But the other people who come, you give them the steak, you say 'How's your meal?', they say 'Lovely'. It's funny – they think everything is fresh. They love it."

And so they do – and so the Steakhouse trade trundles on. You have to take your hat off to them, really: if the prawn cocktails and black forest gateaux can survive the relentless rise of gourmet burgers and frozen yogurts, they can surely survive anything, retro cockroaches in a casual dining nuclear apocalypse. The day before my abortive meal with Richard, I talk to some customers outside the Cranbourn Street branch, opposite Leicester Square Tube. None of them has a bad word to say. Sarah Macintyre, on holiday from Canada for a week, may be the most enthusiastic of all. "I mean, yes, it's expensive," she says. "But look where we are!" She waves at the Hippodrome Casino opposite. "This is the heart of England. We're not going to get to have tea with the Queen, but this is the next best thing".