One Sunday morning in the autumn of 2014, a Brazilian man arrived at London’s Gherkin tower with his young son; the two toured the building at the quietest time of the week for the City’s financial district.

Almost none of the thousands of people who work in the distinctive Norman Foster-designed tower knew it had received a visit from Jacob J Safra, who had just agreed a £726m deal to buy the building.

A person who knows him says the visit was typical of the style of the heir to the Safra banking dynasty — financiers who have long shunned personal publicity.

That low-key approach stands in stark contrast to the extravagant creation they hope to plant on the London skyline.

If Mr Safra gets his way, by 2025 a slender 305m stalk will sprout from the ground close to the Gherkin’s base at 30 St Mary Axe, its bulbous head standing above the angular skyscrapers that dominate the City.

Unlike the surrounding offices, the “Tulip”, also designed by Foster + Partners, would function purely as a tourist attraction, with rotating “gondola pods”, a restaurant and sky bar. It would be the second tallest building in western Europe after the Shard, less than a kilometre away across the river Thames.

The Tulip plans to cater for 40,000 schoolchildren a year © DBOX for Foster + Partners

Mr Safra, 43, chairs the international division of the family’s J Safra Group, named after his 81-year-old father Joseph — who is ranked by Forbes magazine as the world’s richest banker. Born in Lebanon to a Jewish family with Syrian roots, his wealth was estimated by the publication at $24.7bn last month.

The family moved to Brazil in 1952 and three years later established Banco Safra in São Paulo.

Jacob Safra has been closely involved in the Tulip, according to people working on the project; its genesis came out of difficulties in opening the Gherkin to the public on a more regular basis.

The J Safra Group estimates the paid-for attraction could draw 1.2m visitors a year. It declined to give details on the price of the project, how much the entry tickets would be — other than that they would be “comparable to other London attractions”, or how long it would take to recoup the development cost.

Simply another phallic object that London doesn’t need . . . it will be an eyesore that Londoners have to endure whether they can afford to pay for it or not

In a statement, Mr Safra praised the building’s “elegance and soft strength” and its provision of a “classroom in the sky”.

Having won planning permission from the City of London Corporation, the financial district’s governing body, the company must now persuade the mayor of London, Sadiq Khan, to endorse a scheme that has sharply divided opinion.

Among the Tulip’s critics are Duncan Wilson, chief executive of Historic England — the public body that protect’s the country’s heritage. He has called it “a lift shaft with a bulge on top” that would “cause permanent and irreversible damage to the setting of the Tower of London”, which is less than 1km away.

Greater London Authority planners said it would add to overcrowding in the neighbourhood’s narrow streets. They also noted that it lacks free public viewing areas, although the J Safra Group said the education facility would cater for 40,000 schoolchildren a year, who would enjoy free entry.

Tom Copley, a London Assembly member, said the scheme was “simply another phallic object that London doesn’t need . . . it will be an eyesore that Londoners have to endure whether they can afford to pay for it or not”.

The building has equally strong supporters. Peter Murray, chairman of New London Architecture, an independent discussion forum, said the Tulip could take on a similar status to Paris’s Eiffel tower or communications towers such as Barcelona’s Torre de Collserola, also designed by Norman Foster.

He said it would draw tourists further into the Square Mile, in keeping with the London mayor’s strategy of encouraging visitors to travel to different areas of the capital.

“From Wren churches to banking halls and livery halls, the City is a very rich piece of London’s tourist culture and it’s desperately underused from that point of view,” he said.

“The design . . . is a sort of mini-Gherkin, and the Gherkin is a very popular design.”

If developed, the Tulip would form part of the J Safra Group’s portfolio of more than 200 commercial, residential, retail and farmland properties. These also include 660 Madison, location of Barneys department store, in New York.

In London, the group owns a City office building and two West End properties. It rebuffed an approach two years ago by Lee Kum Kee, the Hong Kong-based sauces and condiments group, to buy the Gherkin.

Mr Khan, who quashed plans for another proposed visitor attraction — the “garden bridge” across the Thames, can either approve, reject or “call in” the plan for further scrutiny. The City of London Corporation expects to refer the application to the mayor in the summer. The secretary of state for housing can also become involved in high-profile cases.

If the project goes ahead, its developers have ambitious aims. They promise: “The Tulip and the Gherkin will bring life to the City of London at all times of the day and evening, seven days a week.”

Additional reporting by Andres Schipani in São Paulo

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