Around the courtyard - which will be a public meeting place, similar to the Central Lobby in the Palace of Westminster - will be shops, two restaurants, and a library. Stairs lead up to the first floor select committee and conference rooms - the main one of which, overlooking the Thames, is to be named the Betty Boothroyd Room. Immediately you are into the modern-conservative aesthetic of the place, with English light oak panelling and parliamentary green carpets throughout. The top four floors are given over to the MP's offices, arranged on either side of long oak-lined corridors running round all four sides of the building.

These are somewhat relentless - the constant repetition of elements makes it feel like an upmarket hotel crossed with an Oxbridge college. Most of the offices come in suites of three, with two MPs's rooms placed either side of an interconnecting staff room for up to six people. The staff rooms have opaque glass doors with two clear "peephole" slots at adult and child eye-level. But MPs can choose to close the interconnecting doors and enter and leave their rooms privately. Their doors are of two-inch thick oak with rubber seals. You get the point. These people don't much like being overheard.

There are built-in oak cupboards and shelves, purpose-designed oak desks and circular meeting tables, and classic Eames chairs in polished aluminium and black fabric - a famous modernist design from 1958, by the American designers Charles and Ray Eames, that cost a total of £600,000. Finally, each office has a built-in green leather window seat, recalling the benches in the House of Commons.

Some MPs are more equal than others in Portcullis House, however. There are six bigger offices with better views on the corners and another six up in the steep roof, and these are given to more senior MPs with more responsibilities. The Hopkinses took me up to the Tory MP Archie Norman's new lair high in the roof on the river side. It has its own private staircase and a stupendous view across to the London Eye and the South Bank.

The MPs have the pure luxury of space, but none of the trappings of decadence. There are two shared bathrooms on each level - roughly one for every 25 MPs, not counting their staff - and the lavatories are by the lifts as in any normal office block. Bathrooms and lavatories are plainly fitted out. If you want a coffee, you'll be discouraged from brewing up in your office; every floor has a coffee lounge in its south-east corner. There's no swimming pool and no creche. There is not a painted surface in the place, since everything is either oak or white crystalline concrete, polished to sparkle. It is almost austere.

Now comes the testing time. Will all that clever cooling system work as it is designed to? Will the MPs come to love the place? And what about the roof? Hopkins knows full well that some find it just too overbearing. Over time, he suggests, the roof will lighten, the stonework of the walls will darken, and harmony will reign. But he reckons a quick fix is possible, if the bronze roof is polished up to remove the dirt of the building process. "It needs little more than a going over with wire wool," he says.

So much for detail. The overall impression? A building solidly and conservatively made from the best materials, designed like much of Hopkins' architecture (Glyndebourne Opera House springs to mind) in defiance of fashion. It is not pretty. But it is more than capable of ageing gracefully, and is quite prepared to bide its time. It is more Old Tory than New Labour, but I imagine most MPs will learn to live with that. And it could be by no other architect on earth than Sir Michael Hopkins. That evidence of extreme, even bloody-minded individuality is one of the reasons I like it.