One simple yet brilliant brainwave has guided travellers around London for 78 years. Harry Beck's Tube map is one of the greatest examples of graphic design in history.

Beck was an engineering draughtsman whose radical idea to straighten out and simplify the Underground lines was way ahead of its time. It was pure modernism. And it has lasted, in different incarnations, right up to the present day.

Geographers talk of mental maps – the way in which the human brain understands the space around it. For tourists and visitors – and even Londoners – the city in their mind's eye is shaped like the city Beck depicted using multicoloured lines set at 45-degree angles.

So when an idea for a new Tube map was unveiled by Mark Noad in June this year, feathers were ruffled. "London is my home town so I know the tube system well and the classic 'Beck' diagram has always worked for me," he says.

"But, in recent years, a number of friends from outside London and overseas have told me they found it confusing and made navigating the city difficult for them. The geographical inaccuracies were obviously an issue for people unfamiliar with London so I thought it was worth looking at the map again to see if there was an alternative approach."

So the designer took a brave step – he reimagined the map without Beck's commitment to straight lines. Noad's map looks more like how London looks – with stations placed nearer to their true geographic locations.

Not everyone is enamoured with it. "Noad's design in particular seems to be simply an update of the geographically correct map designs that were ditched when Beck's design came along. "I don't think there's any point in radically redesigning something that's so successful," Angus Montgomery, news editor of the website Design Week, says.

Yet perhaps there is something to love about this map? The London Overground network that loops around the outside of the city makes much more sense on it. As a recent member of the TfL family, its current mapping is not yet up to scratch – and its integration with the current Tube map is shoddy.

And perhaps this points to the real problem. Noad says his beef is not with Beck's original, but rather with the way TfL mandarins have tweaked it: "If Harry Beck saw the current diagram, I don't think he would be happy to put his name to it. So I wondered what he might do if asked to start again with the different parameters we have today." "TfL's tweaks have had varying success," Montgomery says. "I was surprised at how angry people got when the Thames was removed from the map last year. I'm interested in how TfL is going to deal with any new lines that are added to the map – there's a chance they could run out of colours."

Beck's map is a sacred cow. It's more than a map or a diagram, more than a way to find yourself or your friends or your colleagues or your lover, more than a way to understand London's shape. In some ways it actually is London. In a city of such diversity and with so many incongruous forms and so many disparate neighbourhoods, Beck's map is a picture of the single city.

In the wake of the recent unrest, Beck's Tube map is another one of those small things that glues everyone who lives in London together as one – not least because public transport by its nature is used by everyone from commuting City workers to schoolchildren getting to their classrooms.

"We are not rooted to Beck's map because it is iconic, we are rooted to it because it works," says Claire Dobbin, who takes a break from writing a book about the history of the map to provide her opinion. "When it was first introduced, Beck's map embodied the very essence of modern functionalism that underpinned the Underground's design philosophy. It was fit for purpose. It is capable of serving, living and growing with the city it has come to represent. So why change it?" Dobbin, who is also curating a major exhibition on the map at the London Transport Museum next year, adds: "It is one of the most widely recognised maps in the world."

But others are more positive. "I applaud Mark Noad and anyone else who wants to throw their ideas in," says Mark Ovenden, author of the wonderfully entertaining coffee-table tome Metro Maps of the World. "There are a number of other extremely talented map-makers out there too, like Max Roberts – who's produced an entire gamut of styles and solutions to map the Underground." So what about the metro maps of other world cities? Who does it well? Ovenden laughs: "Big question! The Moscow one is funky because they have that wonderful circle line to play with. Tokyo is fun because it's just so mad and busy. Barcelona is probably the most London-esque, with the same ticks for station makers and the same interchange symbols. Most of the German ones are achingly perfect."

Berlin's current U and S-Bahn map obviously tips its cap to Beck. It was designed by Erik Spiekermann.

"My Berlin transit diagram owes a lot to Beck," Spiekermann says. "It works very well for the Tube. It never pretends to work for other types of journeys. The only reason people are using it for everything else is that is appears to be so simple, hiding the whole complexity of London underneath those few lines and angles.

"Most German transport systems imitate Berlin. But they all suffer from information overload."

One question remains. Is Beck's Tube map actually a map at all? Or is it a diagram? "Although I always refer to the design as a 'map' I think I'd agree with Erik Spiekermann that it's technically a diagram," Montgomery says. "Regardless of the semantics, the success or failure of 'map' designs hangs in how they balance legibility and detail and how they address the target audience. In this, Beck's design succeeds admirably."

Noad says: "The semantic debate is a bit of a distraction." Dobbin says: "Short answer? It's a diagrammatic map. It functions as a map – London's travelling public uses it to plan and execute journeys from A to B. It just uses a diagrammatic form of representation."

Beck's map may not appear as perfect as it once seemed – yet, today, it's still influencing designers and map-makers around the world. It is a true classic. But then again it was Beck's own wild innovation back in 1931 that resulted in such a brave leap forward – so perhaps it's time for today's young design guns to think radically about redesigning the Tube map once more.

But could technology eventually usurp maps altogether?