Its entrance is a restored granary, its main thoroughfare a vaulted street. But are Central Saint Martins students happy with their spectacular new home? One term in, Jonathan Glancey finds out

'I was so disappointed," says Carol Breen, a student of communication design at Central Saint Martins college. She's talking about the London institution's decision to leave its old premises, scattered around Soho and beyond, and relocate to King's Cross, a part of the city famous for trains and, well, more trains. "I thought it would be quite sterile," says Breen, "but I have to say, the building is beautiful."

The area, however, although certainly dramatic, could never be described as beautiful – and right now it's anything but peaceful. The college is reached via an unspectacular new bridge over the Regent's Canal; but, instead of the sound of gently lapping waters, there is the pounding of pneumatic drills, the thrum of heavy plant machinery, the sound of digging, lifting, thumping and dropping. Join all the students scurrying across Saint Martins' public square – still very much under construction and so vast it's like a stone prairie – and you start to wonder why one of the world's most highly regarded art and design colleges would ever choose King's Cross at its new home.

Here, 67 acres of former railway lands are slowly being conjured into a newly habitable stretch of city that one day will boast a full complement of shops, flats, offices, cafes, restaurants and performance venues, with Central Saint Martins at its heart. Given that the college used to be housed in a jumble of buildings spread across central London, with its boundless daytime and after-dark attractions, it is hardly surprising that many students (and tutors) found the idea of upping sticks to the former King's Cross Goods Yard questionable and even upsetting.

But there are plenty of compensations, not least the chance to study in a piece of contemporary industrial architecture with great presence. Once through the forbidding gateway – formed by Lewis Cubitt's restored 1852 granary building, a brick and iron colossus whose upper floors house a library – you find yourself in a huge lobby facing a massive enclosed street. This is 110 metres long and 12 metres wide with, 20 metres above your head, a translucent vaulted roof: it's a dramatic and powerful space, set between three-storey ranges of studios framed by two Great Northern Railway goods and grain stores. The sheer scale of it all is wholly unexpected – as if a stretch of street as long and wide as Oxford Street had been roofed over within a building.

"When we won the competition to design a new Central Saint Martins in 2002, the plan was for a new 11-storey block in Holborn," says Paul Williams of Stanton Williams, a practice responsible for some highly crafted and lovingly finished modern designs, from the Millennium Seed Bank in West Sussex to shops for Issey Miyake in London. "But with all the space here, there was no need to build upwards."

Space is certainly the dominant feature. One side of the cavernous entrance lobby leads to art galleries, as yet empty; the other to what will be a strip of shops, cafes and places of entertainment that Argent, the developer of the King's Cross site, hopes to keep as chain-free as possible. And straight ahead is a row of shiny turnstiles that stop the public at the point where the internal street begins.

Look through from here and you see students slowly making sense of the vast architectural canvas enveloping them. Squatting on the floor made of thousands of tiny timber blocks, lying on benches, tapping away at laptops, talking together inside and outside a vast refectory, they seem to be perched like fledglings on some kind of ultra-modern rockface. There is such a feeling of space, of coming together, especially with so many bridges linking the two sides – and this is the whole point of the building. As Breen says: "It allows us to get a picture of the whole college. It's good to be in closer contact with students from different courses."

Khedidja Benniche, an architecture student, enjoys feeling so exposed: "I find being a guinea pig very empowering. I find working in the street or on the balconies inspirational, plus the openness helps. You always see if tutors or friends are passing – although the acoustics are an issue. Perhaps the architects overlooked this."

These sort of imperfections were, however, part of the plan, it seems. "It's still a big warehouse really," explains Williams. "As architects, we've pulled back to allow students and staff to stamp their own identity on the building. So it's a little raw. We think it's up to the various departments here to test the potential of the building. It's utterly unresolved in that sense."

Studios, for just about every creative discipline you can think of, rise up on either side of the street, reached by lifts and factory-like stairs. With all those plain concrete floors, all those rough and ready timber partitions, plus the exposed ductwork, the sewing machines, lathes and looms, it feels a bit like a 19th-century Manchester mill brought up to date. Each studio is tinted and enlivened by paintings, sculptures, clothes, prints, videos – and, of course, students.

"I denounce him before you! Arrest him!" barks a young man dressed in 17th-century French garb. I've sneaked into a rehearsal room: I think it's Molière's The Misanthrope. But drama students and set designers can also get their hands on a fully equipped theatre, a studio theatre and a further set of rehearsal rooms cantilevered out over a lobby bar and set behind a great translucent screen. At night, anyone walking past on the outside will see shadows of the young actors striking poses behind the glass. What's more, the lighting gantries have disabled access – not something you can say of many theatres.

It does seem astonishing, but even when you have tramped through acres of studios, the building just keeps on going. Here, at its far northern end, are lecture theatres. I peep inside. A talk is in progress: "Bohemia in London – Fashioning Artistic Identity." In a central seat sits an upright young man in a pair of sail-like, calf-length black cotton trousers, his head of tightly drawn hair crowned with a top-knot finished in traditional Japanese style. I don't know if he's there to listen to the lecture or to illustrate it.

"What you get here," says Williams, "is architecture as a kind of interchange. I like to think that, whereas in the 19th century this was a place where grain from Lincolnshire connected with the railways and the canal, now ideas are interchanging here between students from all over the world." The statistics do bear this out: 53% of the college's 4,000 students are from the EU (including Britain, of course), with 47% from the rest of the world. I can't resist mentioning the cheap and cheerless red-legged chairs staggered along the internal street. "I winced when I first saw those," admits Williams. "We really have to look for something else when there's some spare money."

That's the Pompidou spirit

Heading back to the main entrance, I visit the beautiful library in the granary building, its many bookstacks squeezed between iron columns painted a lovely deep red. Beneath timber joists, students leaf through books and magazines while enjoying – and hopefully being inspired by – views out to the architectural fantasia of St Pancras. The walls are marked with the remnants of bold Victorian numerals to identify what were originally grain chutes but are now windows. Phil Baines, the college's professor of typography, has used this lettering as the basis for the distinctive typeface that features throughout the building – although such is the clarity of Stanton Williams's plan, there is little need for signs.

Just before I leave, I look back at the monumental spaces the architects have created. Here is a rugged yet heroic place, a fusion of modern design and 19th-century industry that uses space in a way that's reminiscent of Tate Modern. It reminds me, too, of the Pompidou Centre. Posters of that great Paris building, also designed to provide endless amounts of flexible space where anything might happen, are pinned up in the college's architecture department. It's no great surprise to find that Stanton was a member of the Pompidou design team back in the early 1970s: its spirit lives on in this raw, powerful place.

"We see each other all the time, everywhere, which is good," says Andrea da Costa, a textile design student. "You can have a peek into what students of other disciplines, such as industrial design and jewellery, are up to. Fashion and textiles are now on the same floor, sharing workshops, mannequins, sewing machines – and inspiration. The best part is definitely that we are finally on one campus. The students are united – and getting to know each other."