When it opened the developers of the Shard boasted that it should only take “about 20 phone calls” to sell the 10 exclusive apartments near the top of the tower for up to £50m each.

Yet five years on from the Duke of York and the former prime minister of Qatar officially opening “Europe’s first vertical city” with a dazzling laser display on 5 July 2012, all 10 of the flats on the 53rd to 65th floors of the 72-storey building appear to remain unsold.

Brochures for the apartments, which include three two-storey duplex units, boasted that on a clear day residents should be able to see the sea and the grandstands at Ascot from their new perch in the centre of the capital.

The penthouse stands at 735ft, just below the entrance to the £30.95-a-time public viewing deck, which attracts up to 6,000 visitors a day. Even the lowest apartment, which it was hoped would sell for £30m, is higher than any home ever built in London.

But the brochures are no longer available and the tower’s developers and its Qatari owners are reluctant to speak about the residences, which they had boasted would be among the most luxurious in London. As well as the views and double-height entertaining space, potential residents were said to have the luxury of being able to order room service from the five-star Shangri-La hotel below, and call on its maids to turn down their beds. A “back stairs” service lift was shown in floorplans so meals and cleaners could be delivered directly to the apartments’ kitchens.

Baron Phillips, spokesman for Irvine Sellar, the recently deceased property visionary who led the development of the Shard, declined to comment about the unsold apartments. It was Phillips who told the media that several of the world’s super-rich had expressed interest in buying apartments years before the building was finished and said of selling them: “I should think about 20 phone calls should do it, don’t you?”

The view from the 67th floor of the Shard. Photograph: Victoria Jones/PA

Sellar convinced Italian architect Renzo Piano to design the Shard over lunch in Berlin in 2000, with the first designs sketched on a menu. But the project nearly collapsed in the wake of the 2007-08 financial crisis before Qatar stepped in to buy 80% of the tower.

Representatives of Qatar Diar, the real estate arm of the gulf state’s sovereign wealth fund, did not respond to requests for comment. A spokeswoman for Real Estate Management, the property management firm appointed to oversee the day-to-day management of the Shard, said the apartments were still “completely empty shells”.

No apartment sales have been recorded by the Land Registry. Levels 53 to 65 and the apartments’ exclusive entrance on the ground floor were in December 2015 leased to LBQ Four, a Jersey-registered firm believed to be part of the London Bridge Quarter, the holding company that owns the Shard. The 250-year lease valued the 10 apartments at a total of £199,250,000.

Henry Pryor, a luxury property buying agent, said he was not surprised that the Shard’s owners had yet to sell any of the apartments as a sale of one apartment would set a publicly recorded price and make it harder to sell the other apartments for more if and when the London ultra-prime property market improves.

“If they could sell them for what they want for them they would have sold by now,” he said. “If they sell they will crystallise a price and that makes it very difficult for future sales because the benchmark has been set. That is one reason developers chuck in goodies [like cars or fine wine] to keep the apparent price up.”

Pryor said the Shard apartments have not been able to attract prices near the record £136m paid for a flat in the Candy brothers’ One Hyde Park for reasons that any avid watcher of TV property shows would know: “Location, location, location.”

“Kirstie and Phil tell us it every week, location, location, location. Rich people don’t want to shell out zillions living south of the river, it’s a shock enough living anywhere south of the [Hyde] park,” he said. “Nobody knows anyone who lives south of the river.”

The Shard has done better at letting the lower floors for offices, although many have gone to companies owned or partially owned by Qatar. But some whole floors are still to be let, including all 29,824 sq ft of the 12th floor.

The University of Warwick’s business school has rented level 17 and fitted it out with a lecture theatre with perhaps the best student view in the world.

