Your mission, should you choose to accept it, Mr Alexander, is to infiltrate GCHQ, the £800m spy centre cunningly disguised as an immense doughnut. To confuse the guards, you will be posing as a journalist wearing a funny hat. Keep your eyes peeled and tell us what you discover
How do you get a brief, and a PFI brief at that, for an top secret eavesdropping headquarters without everyone getting to hear about it? That's the challenge that faced the project team building the Government Communications Headquarters at Cheltenham.

GCHQ – an £800m building the shape of a giant doughnut – is not only Britain's biggest PFI project, it is the biggest building project in Europe. The scheme is promising to provide accommodation of a very high order and, amazingly, it's about three months ahead of schedule.

GCHQ was established 50 years ago to snoop on the Russians during the Cold War and is essentially a manufacturing operation in which the product is information and the raw materials data harvested from the ether. It is a modern-day descendent of all those tweedy, bespectacled Bletchley Park boffins poring over incomprehensible letter sequences … except that instead of trying to decipher written code, they are monitoring bands of the electromagnetic spectrum. When complete, the doughnut will be stuffed full of sophisticated spying equipment, allowing staff to monitor everything from Al Qaeda's emails to the mobile phone conversations of the rich and famous (the "Squidgy" conversations between Prince Charles and Camilla Parker-Bowles are believed to have been leaked by somebody at GCHQ).

Eighteen months before the centre is due to become operational, I am taken on a tour of the new building – before the security shutters come down forever. So what is it like visiting the UK's most hush-hush construction job?

The reception area is surrounded by Stalag Luft-type barbed wire, but then so are most big construction sites these days. I am not frisked as I go in and there is a distinct absence of mean looking Doberman Pinschers about the place. There is a little pep talk, with the obligatory 10 minutes on how the contractor was carrying out its safety obligations, and not much on what Osama Bin Laden is having for breakfast these days. The PFI representative from GCHQ is cagey about progress, but it appears that the government loves the project, and everything is going swimmingly. When I discover that I have left my security pass in the changing room there is no immediate outbreak of howling klaxons or the clatter of security guards racking pump action shotguns. Instead, our guide just pulls out a spare from his pocket.

Essentially, GCHQ is a purpose-built million square foot corporate headquarters with a build cost of £330m. It happens to be designed for a lot of spooks, but would offer agreeable accommodation for office workers engaged in almost any activity. The James Bond part of the deal is manifested by the vast areas of basement space allocated to the computer equipment (imagine a 4 m high room that is the length and breadth of Wembley stadium, divided into four sections and enclosed within a perimeter blast wall). These days, though, as the architect points out, many big financial institutions have IT demands that are almost as stringent.

I feel the icy silence crackle. Surprisingly, I am not on the list of those who need to know such information

The computer installation, the biggest outside the USA, will be done by GCHQ itself. "And how much will that cost?" I ask the PFI representative. I feel the icy silence crackle. Surprisingly, I am not on the list of those with a need to know such information.

The developer, Integrated Accommodation Services, is a consortium of BT, Group 4, and Carillion – divisions of which acted as contractor, structural engineer, services engineer, environmental engineer, building controller and are even running the cafes, shops and dry-cleaning service. The architect for the scheme is Gensler – a huge US firm that arrived in London about 15 years ago to kick some ass – in the form of design fit-outs for the colonial outposts of American legal and banking megacorps. GCHQ is paying the consortium £800m over 30 years to build and maintain the doughnut.

Christopher Johnson, managing director of Gensler London, designed the 200 m diameter building. It has separate service buildings outside the main circle, which is itself composed of office accommodation on two and three floors either side of a glass-lidded atrium. In the centre of the doughnut is the huge enclosed landscaped garden. There is no access to this except through the rest of the building, so it is secure. More importantly, Johnson has arranged for the structural columns that support the atrium to come through the roof and be capped off. These form a complete ring of flat concrete beds each about 3 m across, so that GCHQ can set up and train listening equipment anywhere in the 360° radius around the centre, which would be invisible from the outside.

The novelty item in this well-thought-out and comprehensible proposal is the provision for day-to-day servicing, which is done by means of an electric train that drives around in the basement service road delivering everything from paperclips to chilled spiced mango at distribution points along the perimeter. With the GCHQ express, "you need four fewer staircases and five fewer lifts", according to Carillion Building's project director Howard Shiplee – another manifestation of the highly practical nature of this circular design.

"So how do you find out what such a secretive client wants?" I ask Gensler's Johnson. "Well, as you go along, you pose alternatives as you would with a normal client," he replies, "until you reach a point where there's a deathly hush. So you rapidly move on to something else. Your clients steal away to discuss the hush-inducing suggestion in secret, and three days later they come back and say 'That's a good idea – we'll take it'."

You pose alternatives, as you would with a normal client, until you reach a point where there’s a deathly hush …

Christopher Johnson, Gensler London

Architecturally, GCHQ is pretty decent – an almost incomparable improvement on the various dilapidated and discoloured concrete concoctions that provide the accommodation at present. The circular frameless glass wall (actually a thermal buffer, as it is not the external weather skin) is described by Johnson as his "veil of secrecy" – and very calm and sexy it is too.

There's nothing like telling a contractor he's going to have to look after something for 30 years to encourage him to jack up the specification, and in GCHQ the client is being well served. Stainless steel ironmongery, hardwood doors, stone flooring in numerous differing finishes in the circular circulation spaces … stainless instead of galvanised steel for much of the mechanical equipment (designed and produced off-site by Carillion) and a sourcing palette from all over Europe for glazing and cladding components.

A slight disappointment is the low level stone wall around the perimeter. This was originally conceived as a vast, almost prehistorically scaled, drystone wall (very Cotswold, very green, very beautiful) but this proved too costly in construction time – as did stainless steel gabion cages. Instead, the base is surrounded in large prefabricated concrete tapering panels with natural stone bedded into the edge and assembled to suggest a giant stone skirt. Perhaps because it is not as beautifully cylindrical as the glass above it, or perhaps it's just too much of a McDrystone wall, but it is not a great substitute. Still, if they smear enough moss, yogurt and cow pat into the crevices designed for this purpose it should soon take on an agreeable organic appearance.

GCHQ Cheltenham has perhaps not as unique a briefing requirement as might be imagined. When all of us can overhear each other on our Mk 8 mobile phones, or GCHQ finds some other way to get the information it wants, there will be plenty of takers for the building. However, I cannot imagine but that the 4400 employees are going to be delighted with their accommodation with its airy atmosphere, its central garden and good retail, catering and sports facilities.

I have no idea whether £330m represents good value for money, or what you compare it with to find out. However, it seems to be motoring along nicely, the construction standard looks high, and the architectural quality is clearly evident. Shiplee explains why, as contractor, the firm chose to keep standards so high. "It's too expensive for us to go back and put anything right, for one thing – you can just imagine GCHQ's computer wizards stopping work while an operative tries to relevel an access floor, can't you? And it's the only advertisement we have for more work."