To use the industry jargon, it is the ultimate “disruptor”. Airbnb, the website that allows homeowners around the world to rent out their spare rooms, has had a seismic impact on the travel market.

Hotel chains are reportedly feeling the squeeze as the US upstart – which has attracted $2bn in funding in less than a decade – eats into their business model by offering travellers the opportunity to “live like a local” and “belong anywhere” in one of the two million rooms and properties that are listed on its site.

The savvy exhortations, which feature in slick adverts on bus stops and billboards across the world’s cities, have helped Airbnb expand at a seemingly relentless pace. Already operating in 191 countries and 34,000 cities, analysts at financial services company Cowen & Co predict that, by 2020, Airbnb hosts will be taking 500 million bookings a night, rising to a staggering one billion by 2025.

It is a truly global phenomenon. Yet, just as Uber’s attempts to shake up the taxi market has met resistance, Airbnb finds itself a victim of its own success as cities and countries wake up to the fact that the cute new kid on the block has been transformed into an 800lb gorilla.

The latest salvo was fired last week when Mark Tanzer, chief executive of the Association of British Travel Agents, warned that the popularity of companies such as Airbnb was leading to such an influx of visitors that there was a danger that some of Europe’s most attractive historic cities would be ruined. “If they can’t get around the city you are going to lose value from tourism, even if the numbers are going up,” he said. “Overcrowding in key destinations is becoming a pressing issue. Without controls, we know tourism can kill tourism.”

In the UK, more than three million people have used the site, while 52,500 people have opened their homes to strangers. A typical host can expect to earn £2,000 in return for renting out a room for 46 nights a year.

Until recently, Airbnb’s rise has been largely embraced by politicians and governments, who were quick to hail it as an exemplar of the “sharing economy”. George Osborne unveiled plans in his last budget that will allow hosts on sites such as Airbnb to earn £1,000 in additional untaxed income by sharing their homes. In March, in a sign that it has truly come of age, Airbnb won a contract to provide a reported 20,000 rooms for this year’s Olympic Games in Rio de Janeiro.

It’s not bad for a company that started life in 2008, when its three founders rented out air mattresses in their San Francisco flat as a way of making money. It is now one of the largest online global travel brands and only Priceline, Expedia, Ctrip, and Marriott drive more online room bookings, according to Cowen & Co.

Luca Florio, an enthusiastic Airbnb host, began using the service three years ago to rent out a spare room in the flat he shares with his wife in the centre of Florence. He said: “We saw it as a chance for cultural exchanges, a chance to talk to people from different countries. It was only after three months that we appreciated it could also be a way to make money.”

Florio said he and his wife could rent out their spare room every night if they wished, but he tries to limit it to 20 nights a month during peak season because it “is not just a business, we want to be free”. Guests come from all over the world: in addition to Spain, France, Austria and Switzerland, Florio regularly hosts visitors from the UK, the US, Australia, India, South America and China. “It’s a kind of alternative tourism, a new opportunity for tourists to gain a different view of Florence,” he said.

Florio appears to be a typical Airbnb host, someone using a valuable resource – a spare room in one of the world’s most loved cities – to make a little money, while learning more about people from other countries and cultures. This is certainly how the company likes to portray itself – a platform that allows the little guy to build up a complementary industry, one that increases the size of the hospitality pie rather than takes a slice from existing businesses.

Airbnb points out that almost 900,000 guests used it to visit Barcelona last year, spending some €740m – nearly six times higher than in 2013. Three quarters of the city’s hosts have incomes below the national average – evidence, the company says, that its business model can expand the economic benefits of tourism to more people and more areas.

When Airbnb arrived in Barcelona in 2009, almost 80% of bookings were in the Old Town. Today, in contrast, almost 70% of bookings are for listings outside the Old Town.

Tanzer’s comments about Airbnb’s expansion having a negative impact on tourism were fiercely rejected by the company. In a statement to the Observer, it said: “It is disappointing – but not surprising – to see attacks on new forms of travel that put money in the pockets of local residents and support small businesses outside hotel districts. Airbnb spreads guests and benefits to more families, communities and local businesses – many that haven’t previously benefited from tourism.”

But the Airbnb phenomenon that is driving record numbers of tourists to certain destinations is not just irking the more traditional holiday operators, it is also inviting closer analysis of the company’s business model.

A report examining Airbnb’s operations in the US, published this year by Penn State University, identified the rise of the mega-operator – people who rent out three or more Airbnb units. The report found that “a growing number of hosts were using the Airbnb platform to operate an unregulated, full-time business. Nearly 30% of Airbnb revenue is derived from this group of full-time hosts. They are becoming bigger and more prominent.”

Other organisations have expressed similar concerns. “There is strong evidence that far from simply facilitating the use of empty spare rooms, Airbnb actually enables landlords to bypass government regulation and in effect run illegal hostels,” Julian Ledger, chief executive of YHA Australia, told a parliamentary inquiry.

Airbnb vigorously rejects these fears, pointing out that it is quick to take action against any hosts who are suspected of breaking the law and trying to avoid the taxman.

Earlier this month, it released data showing that since it began it has collected $85m in tax revenue for cities worldwide. Late last year, it unveiled its Community Compact, a series of pledges to “treat cities individually, help our community pay its fair share of tourist and hotel taxes, build an open and transparent home sharing community and promote responsible home sharing to help make cities stronger”.

The initiative came ahead of a sensitive time: Wall Street expects Airbnb to float on the stock market this year, a move that could see it valued at almost $26bn.

But not all governments and authorities buy into the home-sharing concept. San Francisco has passed a law that permits hosts to rent out properties for only up to 90 days a year. Berlin prohibits users from renting out entire properties, while Iceland has proposed rules that will force some home sharers to register as businesses.

Now, in what could prove the most significant threat to Airbnb’s business model to date, the New York state senate and assembly has just unveiled laws that would bar New Yorkers from advertising their homes on its platform.

“If it becomes law, this legislation would threaten thousands of low- and middle-income New Yorkers with fines of up to $7,500 simply for listing that they would like to share their homes,” Airbnb fumed.

Given that it is a fledgling company yet to establish its bona fides, analysts suggest resistance is only to be expected. But, some day soon, Airbnb may have to face up to who is benefiting from its seemingly relentless expansion.

“There are people who do it just for business,” said Florio. “They buy three or four flats in the city and it’s too much.” Such people, he suggested, were damaging the complexion of historic city centres. “These people don’t care about Florentians, just about tourists.”