Several major European cities ground to a halt on Wednesday as licensed taxi drivers took to the streets in mass protests against the smartphone taxi app Uber.

Demonstrations in London, Paris, Madrid, Barcelona, Berlin, Milan and Rome caused travel chaos and long tailbacks, as taxi drivers protested against the app, which they argue is unregulated and threatens their livelihood.

In London, Trafalgar Square and Whitehall were jammed from the start of the planned "go slow" at 2pm, as thousands of black cabs gathered honking their horns, bringing total gridlock to the centre of the capital, while supporters waved banners and started occasionally chanting: "Boris, out!"

A spokeswoman for Uber, the US start-up which links minicab drivers to passengers via a GPS-based smartphone app, said the protests had boosted new users in London by 850%, as people tried to cope with the gridlock.

But the company, based in San Francisco and backed by Google and Goldman Sachs, came under increasing pressure to be more transparent about its tax set-up.

Taxi associations claim Uber routes its payments through headquarters in the Netherlands to minimise its corporation tax payments in France, the UK and Germany – in a similar manner to Apple and Starbucks, which have found themselves in the firing line for the practice.

Steve McNamara, the general secretary of the Licensed Taxi Drivers' Association – which was joined by the London Cab Drivers Club and the transport workers' union RMT – said the cab drivers were not demonstrating against Uber but against Transport for London.

By using a driver's mobile phone to track a journey and charge a fare on the distance and time travelled, Uber was operating with a meter, he said, which under current regulations only licensed black cabs are allowed to do.

"The problem here is that Uber is operating outside the law. There is no question about that. But someone on high has made a decision to leave Uber alone. Why? It is sinister," McNamara said.

Taxi associations argue that black cab meter rates are fixed, whereas Uber's fares are set by the company, which enables it to charge a "surge" fee during busy periods. They add that they have to undergo criminal checks and medicals, be wheelchair accessible, and pass the Knowledge test, but that Uber drivers need only a minicab licence and commercial insurance.

Transport for London has now referred the matter to the high court. McNamara questioned the issuing of a licence to Uber when its tax status was unclear. "Why do Uber's invoices go through Holland? I don't particularly care if Uber are paying enough tax in the UK, but that is something that should concern Boris."

In a statement, the company said: "Uber complies with all applicable tax laws, and pays taxes in all jurisdictions, such as corporate income tax, payroll tax, sales and use tax, and VAT."

Jo Bertram, the UK & Ireland general manager for Uber, said the number of people downloading the app in London had increased by 850%, compared with the same time on Wednesday last week. "The results are clear: London wants Uber in a big way," she said. "Unsurprisingly, the LTDA, which is stuck in the dark ages, is intent on holding London to ransom and causing significant economic impact to Londoners."

Asked what specific tax the company paid in the UK, and why its invoices go through an office in the Netherlands, she said she had nothing to add to the statement.

Leon Daniels, TfL's managing director of surface transport, said the strike had been "good natured" and he estimated the number of cabs at around 5,000.

"As a result of close co-operation between TfL and the Metropolitan Police Service the number of other road users caught in the congestion was minimised," he said. "The important thing now is continue with the process to get legal clarity on the issue of taxi meters. I hope that the industry will join us in taking that to a conclusion with all due speed."

In Italy, where Uber has been provoking protests from taxi drivers in Milan and Rome since last year, strikes and protests were held not only in the app's two Italian strongholds but also in other cities keen to stave off its arrival.

About 150 drivers protested in Naples, the Ansa news agency reported, while in the northern city of Verona drivers staged a one-hour strike – in solidarity with their Milanese colleagues but "above all against the possibility that the Uber app could spread to Verona too," a statement said.

In Milan, where the strike was due to last until 10pm local time, organisers said the action was about "not surrendering a sector to a multinational which cares about revenue and not service, without even paying taxes in Italy".

Spain saw similar scenes, as Madrid's ubiquitous white taxis began a 24-hour strike to protest against Uber and other similar smartphone apps. The two main taxi associations said 100% of their members had parked their cars for the day in an effort to raise awareness over what they called unfair competition. While taxi licences in Spain cost between €80,000 and €200,000, there is no such requirement for drivers with Uber.

Protests were also held in Barcelona, the only Spanish city where Uber is currently in use. On Tuesday, two months after the app was introduced there, the Catalan government announced it would demand Uber "immediately" cease its activity in Barcelona, and drivers who use it could be fined up to €6,000 and see their vehicles impounded.

Uber has expanded rapidly since it was launched in 2010 by two US technology entrepreneurs, Travis Kalanick and Garrett Camp. The company, which was last week valued at $18bn (£11bn) in an oversubscribed fundraising, operates in London, Manchester and more than 100 cities in 37 countries and has faced opposition in most of them.

It is banned in Las Vegas and Miami and is facing lawsuits in Chicago, San Francisco and Washington, DC.

Speaking from his stationary cab in Whitehall, Carl Williams said cab drivers welcomed competition. "We've been in competition with minicabs for 40 years. This is not about competition, it's a regulation issue: if you want to give Uber meters fine – but, like ours, that meter should be regulated."