This is a bespoke building. It's all about tailoring. Your average spec office block is an off-the-peg number from Next. The best corporate HQs are, in contrast, the equivalent of a Savile Row suit. They fit just so, the cut is impeccable, and they last. What's more, they might well have a surprisingly jazzy lining beneath the carefully understated exterior. And this is what architect Sir Michael Hopkins has given the Wellcome Trust in its new building on the canyon of the Euston Road.

Outside, it is well-mannered and discreet: as invisible as a 10-storey high, 300-foot long, £90m object can be. It's as refined as the ghastly white-and-green new University College Hospital alongside it is crude: a refinement that, if you look closely, is apparent in every joint, every subtle articulation of its gunmetal-grey façade. Inside, it is a revelation.

I arrive in the broad, high-ceilinged reception area, and take a seat beneath a 19th century portrait of the Elizabethan magus John Dee, performing some alchemical ritual in front of Gloriana herself. The Wellcome Trust was spun out of the pharmaceuticals industry as an independent medical research charity in 1936, and gives out around £400m in grants every year with the aim of improving human and animal health, and exploring the ethics as well as the science of the subject. It's big and it's important, both to global health and to the British economy. People arriving in this building with bright ideas are confronted with panels of expert scientists and doctors drawn from all corners of the industry. A programme of exhibitions and performances is laid on for the public. Not exactly your average paper-pushing office, then.

Pretty soon Hopkins - as ever resembling an ambling bespectacled college professor - and his fellow-director Andrew Barnett turn up. Hopkins has pedigree when it comes to this sort of thing. Way, way, back, he was Norman Foster's right-hand man on one of the great radical office buildings of modern times, the undulating black-glass 1975 Willis Faber insurance HQ in Ipswich - now Willis Corroon, and a Grade 1 listed building. Immediately after that, Hopkins quit to set up on his own with his architect wife Patti. Over the years he moved away from the image of high-tech towards something more heavyweight- such as the 1994 Glyndebourne Opera House, or the 2000 building for MPs at Westminster, Portcullis House, hated by many. In fact that one is excellent, ingenious, and looks better all the time - and has one hell of an elaborate façade, induced by the feverish high jinks of Barry and Pugin at the Palace of Westminster next door.

At the Wellcome Trust, however, Hopkins has kept the fussiness well in check. There is a sense that he is returning to first principles. Exposed steel cross-bracing and trusses? Projecting glass stair towers? These are knowing references to the high-tech back catalogue. Here, though, they are absorbed into a greater composition rather than being fetishistic ends in themselves. His mantra - he calls it a "strict code" - is William-Morris-meets-the-Bauhaus: "Truth to materials and honesty of expression". Good to find an architect who not only publishes a manifesto position, but sticks to it.

"It wasn't to be an ostentatious building," says Hopkins as we sip our coffees in the café, seemingly miles beneath the sharply angled conservatory roof of the atrium - itself a structural tour-de-force. "Though it could be a generous one. There was a sense that every penny spent on this could have been spent on research. But then again they'd got to have something which represents them properly as a modern progressive organization."

So cramming in the square footage was not an issue. Given the meetings culture of the trust, so far removed from a conventional back-office operation, the space not filled with desks was if anything more important than the space that was. So as you wander around, you come across little two-storey mini-atria, some linking levels via spiral stairs, where informal meetings can take place. Those are in addition to the series of maple-clad main rooms, backing onto the main atrium, where the big discussions take place and the future of medical research is decided.

The whole place has an air of unhurried efficiency and effortless logic about it. But for me, the Hopkins attention to detail comes out best in something you don't really usually notice much: the handrails. The ubiquitous glass balustrades are much in evidence, but they are in sparkling prismatic glass rather than the usual clear sheets. And instead of the clichéd stainless steel or aluminium rails you normally find topping those sheets of glass, Hopkins has installed fat solid beech handrails cut to precisely the most comfortable angle to lean against. It's only a tiny thing, but it is the accumulation of such details that add up to one very accomplished building.

Many another wealthy organization would have moved its front door to somewhere a little more salubrious than Euston. But Wellcome has always been there, did a land deal for its new building, and wants to stay there. Even Hopkins' attempt to put the main entrance on the quiet, agreeable and now much-upgraded Gower Place behind, facing University College London, was ruled out. Looking that way, it's Bloomsbury. The building steps down to six floors, the environment is more welcoming, you get into the atrium sooner, there to witness a staggeringly complex full-height Thomas Heatherwick sculpture of drifting clouds of dichroic glass balls caught in shimmering wires. Moving the entrance to the back is what the building, as conceived and built, clearly wants to do. But no: Wellcome is adamant that it always has been and wants to remain, forever Euston.

"Every time I come here, I think: what are we going to do about the Euston Road?" sighs Hopkins as we gaze out at the rushing, eerily silent traffic a few feet away, heading for the underpass like water down a plughole. "It's a numbing experience." He supports plans by Sir Terry Farrell, drawn up for London mayor Ken Livingstone, to tame the Euston Road, turn it into a more civilized boulevard, lose that bleak underpass-intersection. But for the 500 staff of Wellcome and their many visitors, once they're inside, the roaring road might as well not exist. All sound is screened out. A few floors up, you're not aware of the road at all.

This is the pleasure of the Wellcome building: it is a self-contained ocean liner of a structure, large enough to be urban in its own right. Atria are two a penny but it's impossible to stand and look down into this one without being impressed by the sheer nobility of the space. Outside, Hopkins has turned to classical proportions, with a clearly identifiable base, middle and top, sliced vertically into five distinct bays. In the end, Hopkins is in the architecture game for the pleasure of working out such slightly abstruse matters. Things that are too subtle for most people to notice. As he says, "That's where we get our jollies from."

This, I promise you, is another Hopkins slow-burn success. He is a craftsman architect with the eye of a jeweller, and he's on top form. Today, the Wellcome building is just there, biding its time, happy not to be a landmark. But in a few years, people are going to say, blimey - that's good. And they'll be right.

www.hopkins.co.uk - a master architect at work
www.wellcome.ac.uk - a world of vital research