The boat obsession of such architects is an undoubted techie fetish, but here you can't fault it. The task is twofold. The first task is the ship-in-the-bottle exercise. A temporary enclosure is needed for up to five years while the famous 135-year-old Greenwich racing tea clipper - now falling to pieces after exactly 50 years in an open dry dock - is painstakingly conserved. Why not, argues Grimshaw, make that enclosure something powerfully attractive in its own right - a place that will draw visitors to watch the restoration?

Task Two, the follow-up to that, will be a permanent building. Once restored the Cutty Sark will once again be displayed out in the open - but this time raised up as if sailing out to sea, suspended in the glass roof structure of a new building. It will allow you to walk right under the keel and get a porpoise's-eye view of one of the most functionally beautiful ships ever built, floating in air right above you.

The man Grimshaw has put in charge of this job is the most serious yachtsman in the office, who also happens to be its managing director: Chris Nash. When he is not being a top architect, Nash is a qualified coastal skipper. He was born by the sea: his childhood was filled with the sound of foghorns. Any other maritime connections? Well, yes. Richard Doughty, chief executive of the Cutty Sark Trust, approached Grimshaw after hearing him in boat mode on Desert Island Discs. The Cutty Sark Trust is anything but wealthy. But then, as Nash points out, the Eden Project was also impoverished when design work first began. So once again, the architects are working at risk. This time, the main source of funding being approached is the Heritage Lottery Fund.

The Cutty Sark may once have been a ship and still looks like a ship, but it is not a ship any more. Its years in dry dock in what is now the Greenwich World Heritage site have turned it, officially and actually, into a building. A Grade I listed monument, to be exact. Its iron ribs have corroded badly and started to go out of shape. It can be shuffled around a bit on land, but it can never go back in the water. "There's a school of thought that says it should be floated off again," remarks Nash. "That's crazy. It would sink like a stone." Note the "it". Nash would say "she", I'm sure, if he thought this was a potentially seaworthy vessel. This difference - being a monumental building rather than a ship - is important. Ships are eligible for HLF support, but other conservation organizations prefer buildings and their contents. The bid is in for £11.75m, roughly half the cost of what will eventually be a £25m project. Most of which goes on the conservation work rather than the architecture.

For the money, this is one of the more interesting architectural projects to come along for quite a while. Take that inflatable enclosure, which the Grimshaw team has developed with engineers Adams Kara Taylor. It's based on the Swiss-invented "Tensarity" structural system of rigid pneumatic beams. Nobody has done much with inflatable buildings for years, now suddenly the technology has taken a huge leap forward. They are playing around with the shape, but at the moment it's something that itself looks like a translucent upturned ship's hull or - if you're being a bit fanciful - a giant Nelson's hat. Nash sees it more prosaically. "It's a temporary shipyard," he says. There'll be real guys working on real bits of the ship in there. A maritime industry back in Greenwich again."

When you go forward a few years and look at the permanent building, it is no less progressive - though more reticent, since the restored ship will be the visual attraction. It is a complex project also involving opening up the interiors of the ship - which were incorrectly restored in the 1950s. But essentially, the roof of the building (which is the existing sunken dry dock, perhaps extended towards the river) will be the hull of the ship itself, suspended in a near-invisible Kevlar hammock. From the outside, what you will see is not the building but the ship, rising higher than before, ploughing through a kind of glass wave. It can be done: they have found a firm of glass-makers in Venice who can make the big double-curved pieces of glass required.

Architecture will thus talk to naval architecture in a glorification of the technology transfer that has taken place between the disciplines in recent years. It means that the ship becomes more than just a bit of the Greenwich landscape, set in a currently bleak plaza, to gaze at casually on your way past. It becomes something more appropriately immersive, drawing in many more people. The Grimshaw designs now need to be combined with Greenwich's other landscape improvement plans for the area. And what's the alternative, after all? The Cutty Sark, last of the tea clippers, is crumbling and will have to close for good in 2007 if restoration does not get under way. And then what? "It would disappear into a pile of rust and sawdust," says Nash. "And I don't think the nation wants that."

Cutty Sark website: www.cuttysark.org.uk
Grimshaw website: www.grimshaw-architects.com