A third of New Yorkers think about September 11 every day

Five years after the shadows of two planes passed over New York, heralding the shattering destruction of the Twin Towers and the massacre of thousands inside, almost two thirds of the city's residents remain "very concerned" about another terrorist attack, a survey shows.

The poll, by The New York Times and CBS News, exposed deep anxiety in the city, with almost one in every three people saying they think about what happened on 11 September 2001 at least once every day.

Nearly 50 per cent said they thought about it once in a while. It also revealed widespread distrust of President George Bush's claims that America was safer than five years ago. Yesterday the main developer at Ground Zero, Larry Silverstein, unveiled of plans for three huge towers that would line the eastern edge of the site and help remake Manhattan's broken skyline.

Distinctive from each other in form and size, they have been designed by Britain's two leading architects, Richard Rogers and Norman Foster, and by Fuhimiko Maki of Japan. While most of the attention so far has been focused on the signature Freedom Tower that will soar 1,776ft from the northern edge of Ground Zero and on the accompanying Memorial Museum, the three towers presented yesterday will not be pigmies and will cost $7bn (£3.7bn). The structure designed by Lord Foster, with a roof composed of four sloping diamonds, will be as high as the Empire State Building.

The authors of the poll do not give reasons for the continuing high level of anxiety in New York but several possible explanations present themselves. Reminders of 9/11, when lower Manhattan became a zone of almost unimaginable slaughter and grief, keep coming, thanks to a steady drip of related media stories as well as big-screen and television films.

Nor has the real-world fallout from the tragedy ended in Manhattan. This year, forensic experts have found more than 700 remains of victims in the Deutsche Bank building, a 43-storey tower next to Ground Zero that is awaiting demolition. This week, another study showed 70 per cent of the workers who toiled for months to clear rubble from the site face long-term health problems.

So far only one new building has been completed at Ground Zero, 7 World Trade Centre, owned by Mr Silverstein. Foundation work has just begun on the Freedom Tower and the Memorial. The former should be completed in 2011 and the latter in 2008.

The masterplan now emerging is much different from that envisaged originally by Daniel Libeskind. The trio of buildings seen for the first time yesterday still faces hearings and may go through considerable change. The tallest, by Lord Foster, with 78 floors, is likely to attract the most scrutiny. The Lord Rogers tower will have an exposed web of diagonal beams, a common feature of his buildings.

On Wednesday, a stop-gap museum called the 9/11 Tribute Centre was formally opened by the Governor of New York, George Pataki, and the city's Mayor, Michael Bloomberg. On two floors in a building alongside the pit, its exhibits include photographs of victims and artefacts ranging from a gun melted into a ball of metal and a twisted window from one of the aircraft.

How willing people will be to work in the new structures at the site is an open question. The New York Times poll found nearly 60 per cent of respondents said that they would be unwilling to work on a high floor of any of the new buildings.

The poll also found important nuances in attitudes towards terror, with people outside New York City expressing far lower levels of concern. There were also striking partisan differences, with Democrats far more likely to be sceptical of the government's anti-terror efforts than Republicans.

The worry expressed by New Yorkers is barely diminished since the days immediately after 9/11. Today, 69 per cent are "very concerned" about another attack, compared with 74 per cent in a poll in October 2001.